The idea is to add fatigue.
Basic idea fatigue is a stat, that you ideally want low.
You get fatigue by doing strenous things (swimming, flying via skill, attacking, moving a lot).
You lose fatigue by resting - this can basically be measured by the character having an action and not actually doing anything. Certain magic potions could also reduce fatigue.
I'd suggest that movement speed should be redone under such a system - movement speeds would vary less, but that amount of fatigue you gain by moving is dictated by how much stuff you are carrying.
If not carrying much, you wouldn't get much fatigue - thus, a lightly equipped person could run around all day and not have to rest much.
If you're near you weight limit, you'd get fatigue pretty often.
Running isn't covered special here - it would fall under movement, but that fact you move whenever you can when running basically means you'd never be resting at all, thus only gaining, never losing.
For certain skills, if your fatigue was too high, you could no longer use that skill (have to stop flying, may drown if swimming, etc). Your max fatigue should perhaps be based on constitution and maybe level (don't get fatigued as much at higher levels).
For the normal case of just attacking/running around, one idea is when fatigue gets too high, your speed starts to go down, but at the same time, you start losing fatigue (in a sense, game is enforcing idea that you have to slow down). One way to handle this might be that if fatigue is to high, player doesn't get as much speed as they should, but loses some fatigue.
High fatigue would effect many things - to hit chances, AC, casting spells (like spell encumberance). Really high fatigues could start adding effects like confusion, etc. Maybe even as part of this, you would apply incorrect items.
I'd say there should be no upper limit of fatigue, just at too high, the effects are bad enough that you'd really want to rest the character.
In game resting (chairs, beds) could be added to regain fatigue faster.
When during certain things, even staying in one place, fatigue should be gained (swimming or flying). If weather effects are used, they could also contribute to fatigue (sitting in the middle of a desert is going to have adverse effects even if just sitting there)
Magic effects could be added to temporary or permanently reduce fatigue. In terms of temporary effects, this would be a straight subtraction (500 fatigue points removed), but when it expires, you go up 500 points from your current fatigue, sou could have a lot more than when you drank the potion.
Perhaps coffee could temporarily decrease fatigue, but after a period of time, the fatigue rushes back plus some (energy crash after caffeine depleted)