So I think I just came up with a pretty feasible and unique, at least for an FPS:
The player can be affected by weight gain, and it will be separate from damage, but health will be more like stamina in a way, still functionally basically like health, but you lose more the bigger you are, functionally the opposite of armor. So at first, you’d worry about your weight, as most attacks early on won’t do much stamina damage, getting too fat makes you a veritable sitting duck, even low level enemies taking decent chunks out of you.
“So I’d just wanna avoid getting fat, right?” Well yes, but actually no! Why? UPGRADES!
The main gimmick, not too dissimilar to @Chubberdy’s Spacethumper, is to use your weight to purchase upgrades, be it movement speed, damage, reduction in damage at higher weights, and several other things that could lead into very interesting builds that would be…
wait for it…
Worth the Weight! 
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