I think that would be quite paradoxical, because stamina increases your encumbrance / max weight capacity.
Well... yeah. Sort of. I think it makes sense for the two to be interlinked (though that would tend to make one... *gasp*.... redundant). Imagine a nominal maximum encumbrance of 300 units. Establish a "comfortable" encumbrance at, say, 150. Anything up to that has no effect on stamina. As soon as you go over that, it starts burning stamina. Make the effect tiny at first, so that in normal play it still wouldn't be noticed - only if you ran a lot or jumped a lot or did a lot of power attacks or whatever would it have any noticeable effect, and that just that your stamina would decrease a wee bit faster and replenish a wee bit slower. But as encumbrance increases, the effect it has on stamina increases. Set it so that at, say 250, it'd be a noticeable effect - you'd be able to see that your character is burning through stamina abnormally fast (and by the bye - I think that encumbrance should be "under the hood" - the way you know you're approaching max encumbrance is by the effect it has on stamina). Keep accelerating the effect until you get to the nominal maximum of 300, and at that point, your character runs out of stamina and can't move - he's using every bit of his energy just to support his own weight and the weight of the stuff he's carrying and doesn't have a bit left over to so much as take a step. (*edit - or at least dramatically reduced movement - see below)
And then, yes, increases in max stamina would equal increases in encumbrance - the new maximum would be, say 350 units and the new comfortable level 175. Boost stamina again and the new maximum is 400 units and the new comfortable level 200. And so on.
Or something like that......
I like that Idea a lot... except for the not being able to move part. Maybe if they did a severe reduction to movement speed and jump height (like -%50) would be better.
It would scale parallel to the amount of fatigue remaining but when you reached 0 fatigue, it would be -%50 instead of not being able to move at all. And maybe once you reached %0 you couldn't get rid of the -%50 speed/jump until you recovered at least 5% of your fatigue.
Eh. Personally, I detest the idea of still being able to move at zero fatigue, but I don't think I could say any more on the subject without being insulting, so I'll just leave it at that. And while if I had my way about it, zero fatigue would mean zero movement, I'm sure Beth won't do it that way anyway. So yeah - alter the scale however necessary so that you can still move with zero fatigue and I would guess that that'll be about the way it'll work.