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Description
This is a new version of my old mod by the same name which I released on Skyrim LE. This mod allows you to use the sprint key to run while you're over encumbered, or just walking. If you're over encumbered, your stamina will drain, and your speed will be reduced, based on how much you're over your carry weight limit. If your stamina is depleted, the spell is removed. You can customize the penalties. Details below.

It works by adding a spell to your character when you press the sprint key that boosts your speed when you're over encumbered. When you release the sprint key, the spell is removed. Your initial bonus speed will decrease the more weight you add, and your stamina will drain more as well. 
This is handled by a spell that detects weight changes in your inventory when you're over-encumbered. No OnItemAdded Events. No polling. The scripts are lightweight.

Customization
If not using the MCM, type the commands on the next page into the consol, where xx is the new value, without the quotes. Re-activate the mod with the More Natural Encumbrance Toggle lessor power if changing the Initial Speed Bonus.

Initial Speed Bonus:
"Set SprintWalkSpeedGV to xx"
Default is 350

Stamina Drain Per Weight:
"Set SprintWalkStaminaGV to xx"
Default is 0.5

Speed Penalty % Per Weight:
"Set SprintWalkSpeedPenaltyGV to xx"
Default is 0.25

This is also explained in the config book in game.

So, as an example, on default settings, if you are 100 over your carry weight limit, your stamina will drain by 50 per second, and your speed bonus will be reduced by 25%. If you are 200 over your weight limit, your stamina will drain by 100 per second, and your initial speed bonus will be reduced by 50%.

Compatibility
This mod will conflict with mods that use SetAv to change your characters speed in game, rather than ModAv.

Requirements
SKSE64

Installation
Before installing, or activating, be sure that the Toggle Always Run setting is switched on.
Extract to your data folder, and check in your load order.

If updating, de-activate the mod first, make a new save, install update, then activate again.

UnInstallation
De-activate in the mod with the lessor power, and uncheck in your load order.