With default settings, upon level up all 3 attributes are increased by 1 in addition to regular level up rewards. Specifically changes will be applied after you choose a stat to increase during the normal level up process and then close the menu. This is unavoidable, as it's the only time a script can tell if the player has leveled up. 
You can have all the above features without SkyUI/MCM.

All features take effect after leveling up or closing all menus:

• Toggle all mod features in MCM
• Option to remove stat alterations, recommended to use this prior to uninstalling the mod.
• Set how much of each attribute to lose or gain each level. Set to 0 to disable that stat.
• Force calculate stats button. Will trigger the script to calculate the bonus stats for your current level with the given settings when you exit all menus, rather than having to wait for the next level up. Use this when installing mid playthrough. 
• Stats are calculated retroactively based on your current player level
  

Compatibilty:

Compatible with everything, can be added and removed at any time (updating this mod on a save that used an older version of this mod, may cause issues, but should be fine, backup your saves). May contribute to save bloat, as do all scripted mods. There are 3rd party tools to clean your saves. It's generally not an issue for most users.
Calculations are based on the actor value; actor level. So anything that introduces a new leveling system that does update the vanilla level value will not work. Im pretty sure no mods like that exist, as that would be a terrible way of implementing such a mechanic.

Fully Compatible with EnderalSE.
According to commenter staera it also works in oldrim!

Designed to run alongside my other mod, Golden Progression: https://www.nexusmods.com/skyrimspecialedition/mods/49140
I also recommend RimStats by KingTroller. It will allow you to view most stats.

As requested here: https://forums.nexusmods.com/index.php?/topic/9828133-a-mod-that-allows-stats-to-increase-by-themselves-per-level-up/

more details here: Better Leveling Devblog
Update 0.3: https://digineaux.com/balanced-leveling-0-3-update/
update 1.0: https://digineaux.com/balanced-leveling-0-3-update-2/
update 1.1: https://digineaux.com/balanced-leveling-0-3-update-2-2/
update 2.0: http://digineaux.com/balanced-leveling-v2-release-2-0

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Want to see how it's made? I'm creating a scripting tutorial showing you how i made this exact mod step by step: