If you wanna be technical it would require both STR and CON to represent carry capacity (even with high resillience you can't carry much if your too physically weak).
Personally i would stick with STR becase A: as noted you still require some muscles to carry the stuff, especially if it is over long periods where your muscles get strained.
And B: Mechanically it gives you incentive to invest in STR even when your not playing a STR based character. Even if your playing a mage or an AGL character, putting points into STR is useful sense you can carry more stuff. CON has already a lot of advantages that makes people want to invest in it.
This makes it more interesting when creating a character when every attribute has good perks for being good at it, rather than focusing on 1-2 "godstats"
Beware the fey!