Maybe that weight should be expressed in a speed debuff.
Akktschually...
...heavy weight (like for armor) does NOT make you run any slower. It just makes you tired a LOT sooner.
And, well... people in heavy armor do not have the perks of medium armor in regards to stamina regeneration, so... that kinda is in the game, sort of?
Although, I personally would love to see an "athleticism" world skill line that has additional sprint, swim and jump buffing passives - with effects that get -diminished- by every piece of heavy armor worn until they are completely nullified in full plate! (Aka, for example, spend 1 skill point for a 7% reduction to sprint cost, -1% for every piece of heavy armor)
Of course, I personally would -also- love to see stamina costs and a "armor" debuff for swimming and jumping in general. To be migrated by just that above mentioned passive line, perhaps?
But I guess that is me, I like things immersive, like not being able to -swim- in heavy armor, and maybe having to take it off when having to take a splash...