Leveling up happens as in vanilla, but with three significant changes:

• Excess progress is not wasted. Any excess progress toward attribute multipliers at level up is not lost but carried forward to the next level. This includes progress in excess of what's needed to receive a 5x multiplier.
• Non-max multipliers are not wasted. Choosing an attribute at level up that doesn't have a 5x multiplier (other than Luck, by default) allows for progression of the attribute via skill increases up to what it would have been if the multiplier had been 5x. If that attribute has already received sufficient increases at level up to reach 100 via additional skill increases, that additional potential is applied to other attributes instead.
• Health is gained retroactively. Health is calculated as if the maximum possible endurance increase was applied as early as possible, up to the current endurance value. The eliminates the penalty for not getting 5x endurance increases each level as early as possible. This is optional, see below.
  

Some implications of the the above:

• Luck will never increase unless it's selected at level up (or unless governing attributes have been changed, see below). It's the player's decision whether to increase Luck or not.
• Characters with lower starting endurance and strength will still have a smaller total maximum health. This means there's still a small tradeoff between different races and classes, as in vanilla.
  

Optional Retroactive Health Calculation:
The retroactive health calculation can be disabled via the mod config menu, to allow the use of another that provides a different health calculation. Set to "Off" in the MCM and follow the instructions of whatever mod you'd like to use in its place. To go back to the included retroactive health calculation, simply change the setting and reload the character; health will be recalculated when the character is loaded.

Enhanced Level Up Progress Tooltip:
This mod adds the option to display an enhanced tooltip similar to the MCP tooltip (if the MCP tooltip is enabled, the new tooltip replaces it). To enable the enhanced tooltip, visit the Mod Config Menu; it is disabled by default. This new tooltip adds the following information for each attribute:
Attribute (base/potential) level_ups
base - the current base value of the attribute
potential - how high the attribute can be raised via skill increases without gaining another character level
level_ups - the number of related skill increases; this could be negative if an attribute has been increased without sufficient skill increases at character level up (based on 10 / iLevelUp10Mult), or it could be a fraction (rounded to nearest 0.1), if iLevelUp10Mult has been changed such that 10 / iLevelUp10Mult is not an integer.

Tooltip Example:
Strength (41/45) -2.0
This character added 1 to strength at level up without any strength related skill increases. He now has to "pay" for that strength increase with 2 strength skill increases, to bring him to 0. After that, he can increase strength up to 4 more times (up to 45), with 8 additional strength skill increases (maintaining the vanilla 5/10 ratio).

Examples:

Excess progress:
As of level up, you've raised skills governing personality (2 skill increases), willpower (5), strength (2), and intelligence (1). You choose to increase willpower, personality, and luck. In vanilla, the progress toward strength and intelligence would be set to 0. Instead, we preserve it and you start the next level with strength (2) and intelligence (1).

Non-max multipliers:
What happens when you choose a multiplier that's not x5? We'll look at willpower from the scenario above. You have 5 willpower skill increases and you choose the x3 multiplier. In vanilla, that's it: you've lost the opportunity to have x5 instead of x3. Instead we track what your willpower would have been if you had received x5 and allow it to increase via additional skill ups, up to that point. Normally, you'd get x5 if you had 10 skill ups. We only had 5, so we'll need 5 more to add 2 to willpower. The following table shows how willpower will continue to increase after level up when additional willpower skills are increased:

skill ups | willpower
 6
 7
 8          +1 (4)      
 9
10   +1 (5)

Any skill ups past 10 are counted toward your next level multiplier. It's all cumulative; if you level up again before getting the additional skill increases, they will still be available, and if you increase willpower further at level up with a non-max multiplier, you'll be increasing the point to which you can raise willpower via additional skill increases.

The above is implemented with a hidden cap that tracks what your willpower would have been if you had gotten x5 multipliers every time you chose willpower at level up. What happens if that cap is at 100 (or would go over 100) and you choose willpower again? In that case the excess is applied to other attributes, starting with those that have the most progress toward a multiplier. The same rules above apply: that attribute will only increase when governing skills increase, unless it is explicitly chose at level up. Because progress is never lost, it is possible to receive extra attribute increases immediately after level up.

This is the one point where this mod deviates slightly from vanilla, in that in this case you can get an attribute increase without ever choosing it at level up. I felt this was a reasonable trade off, given the alternatives: either requiring the player to be aware of and track how often a given attribute has increased at level up, which is not at all in the spirit of this mod, or not allowing further attribute increases at level up when this cap was reached, which takes away player choice. It's not perfect, but I felt it was the best option of the three. In any case, your character still progresses at the same rate as in vanilla, and you don't receive anything you haven't earned.

Here's an example of how this works:
You've already raised willpower enough times at level up such that this cap is at 100, but the actual value of the attribute is not yet 100. You choose willpower at level up. Instead of raising the willpower cap further, it's instead applied to other attributes starting with the one with the most related skill increases. Let's say that you've been raising strength skills , but never choose strength at level up. You now have 8 strength skill increases, and 0 for all other attributes. The cap increase will apply to strength, increasing it by 5. Since you already have 8 increases all of them will be used to raise strength by 4 points immediately. If you raise strength skills twice more, you'll get an additional +1 strength. After that, strength progress counts toward the next level up multiplier, as before.

Retroactive Health:
Your character has 40 each starting strength and endurance, and thus 40 starting health. You reach level 5 without ever choosing endurance at level up, and your health is now 56. When you reach level 6, you get a 5x multiplier and add 5 to endurance. In vanilla your health is now 60.5. Instead, we apply the extra 5 endurance as early as possible, in this case level 2, and recalculate your health as if you always had 45 endurance starting at level 2, giving you 62.5 health. At level 7, you get another 5 endurance. This time, it's applied at level 3, since we've already applied the max at level 2, giving you 69.5 health total.

Existing Characters:
The recommended way to play this mod is with a new character, but it can be added to an existing game if desired. However, any lost progress or non-max multipliers prior to adding the mod cannot be recovered or otherwise mitigated.

GMSTs and Balance Mods:
This mod was designed with vanilla settings in mind, but it should be compatible with balance mods that alter progression by tweaking the GMSTs that affect leveling or by changing skills' governing attributes.

Governing attributes are checked as needed, so any changes made via an ESP will be honored by this mod. If Luck is added as a governing attribute to one or more skills, then it will be treated as the others when it comes to multipliers and skill increases. Conversely, if another attribute is removed from all skills, it will be treated as Luck in vanilla.

This mod uses the following GMSTs directly and will honor changes made to them via ESPs (and scripts, in most cases):

• iLevelUp10Mult determines how quickly attributes rise relative to skill increases. In vanilla, this has a value of 5, resulting in 1 attribute increase for every 2 skill increases.
• fLevelUpHealthEndMult determines the percentage of endurance to add to health each level.
  

The remaining GMSTs influence how character progression happens. Changing them will have the same impact as in a pure vanilla game.

Special note on iLevelupMajorMult* and iLevelupMinorMult*:
There's a bug in the engine that causes these GMSTs to be applied incorrectly to skill increases received via NPC training and skill books. If these have been modified and the bug fix is not present this mod will be disabled, with a message on screen and in the log. The fix can be downloaded here.
You do not need this fix to play this mod with vanilla settings.

Morrowind Code Patch:
The MCP adds three options that are relevant to this mod.

• Interface changes -> Level-up skills tooltip
  This shows the number of skill increases linked to each of your attributes. In some cases, after receiving a skill increase the relevant attribute count will not increase. This is due to the way skill and attribute increases are tracked in this mod, and the game's inability to properly handle fractions or negative numbers for these values. This is just a display issue; everything is handled correctly behind the scenes. Alternatively, enable the enhanced tooltip in the Mod Config Menu to replace this tooltip.
• Game mechanics -> Attribute uncap
  This allows increasing the eight main attributes past 100. This mod will detect this setting and should behave appropriately, but this has not been extensively tested.
• Game mechanics -> Skill uncap
  This allows leveling of player skills past 100. This should work with this mod, but has not been extensively tested.
  

Final Thoughts:
This mod is not for everyone. Some will want a more complete overhaul and rebalancing of the leveling system, which this does not provide. Conversely, I'm sure there are some who prefer the pure vanilla experience, either enjoying the process of meticulously planning skill increases and progression, simply taking progression as it happens with all that implies, or landing somewhere in between.

This mod is the spiritual successor to the "Automatic Leveling" mod I posted on the Bethesda forums a few years ago. I don't know if it saw much use, but building that mod was my primary motivation for tinkering with the MWSE source code.

Requirements:
Note: This mod uses the pre-release 2.1 branch of MWSE, currently in development.

This mod requires Morrowind Graphic Extender (MGE-XE) 0.10.1 or later and the latest nightly build of MWSE.

Installation:
Extract the archive into .\Data Files in your Morrowind installation directory. The mod should contain the following files:
.\Data Files\MWSE\mods\merz\improved_vanilla_leveling\main.lua

Using this Mod:
There is no esp file to activate. Simply install the MWSE 2.1 and this mod, and load up an old or new game. A new game is recommended, see above for further discussion.

Removal:
Delete the .\Data Files\MWSE\mods\merz\improved_vanilla_leveling folder.

To remove the extra character data, extract the Cleanup archive into .\Data Files in your Morrowind installation directory. Contents:
.\Data Files\MWSE\mods\merz\improved_vanilla_leveling_cleanup\main.lua

Load the game to clean. When prompted to remove the data, select remove. This cannot be undone. Save the game. When finished, delete the .\Data Files\MWSE\mods\merz\improved_vanilla_leveling_cleanup folder.

Known Issues

If using a mod that changes levelupsPerAttribute without triggering a custom event (e.g. anything using Skills Module, Ashfall, etc.), any attribute increases that should arise from that skill increase will be delayed until either you raise a vanilla skill that shares the same governing attribute or your character levels up. Progress is still tracked and accounted for correctly.

If those mods add a custom event to signal that their custom skill has been raised, I could incorporate that event here and treat it like a vanilla skill increase. Until then, this is the best that can be done, without doing something excessive like checking every frame.

Incompatibilities & Save Game Warnings

This mod should not be used with other leveling systems. It may be compatible with mods that adjust progression via GMSTs, see above for further discussion.
This mod adds a small amount of data to the save file via lua. To remove this data, see above.