I'm assuming I need a mod to fix this, as I have seen no other way, but is there any mod that makes it so that unequipping armour when you are close to the encumbrance limit does not give you an encumbrance penalty, usually resulting in you barely able to move? Or an equivalent mod? There are many times where I want to take a piece of armour off or just wear normal clothing but then I end up unencumbered - the only solution I know of being tgm.

Hmm well in that case does anyone know if they think it's doable/relatively easy? If so I may consider modding it in myself

The other solution being putting the armor back on.

It's not that you are getting an encumbrance penalty for taking off the armor. It's that the weight of armor you're wearing does not (entirely) count against your encumbrance limit. There's a light armor perk that makes it so that armor you wear doesn't weigh you down at all. Heavy armor has a perk that reduces the weight of worn armor.

Hmm well it would be nice if wearing normal apparel could also not count, but as it is not armour I don't think there's any vanilla way of ensuring that.

I'm not sure, but normal apparel is probably not counted against your encumbrance limit. It's just that when you move armor into your backpack, its weight gets added back to your encumbrance limit.

That explains it; I've been wondering how and why it works that way. However I've now discovered the only reason I'm having an issue with this is because half of my mods (one of which includes encumbrance rebalancing for certain objects) keep unchecking everytime I start the game. Problem for a new thread I guess.
Edit: Making the appdata/skyrim folder read-only seems to have done the trick. This thread feels somewhat redundant now