I'm looking for a mod that made it to where the armor you wore did not count fully against your encumbrance, like it only weighed a fraction of it's actual weight.

There are perks in both the light and heavy armor skill trees that make worn armor weigh nothing.

For light armor, the requirements are low. If you are buffing light armor, you will get the perk pretty early.

For heavy armor, it requires more skill points to get.