I'm only just above 'Spaghetti arms' in terms of physical size, and I don't have problems. I don't think being muscular would mean that you would play slower, but I do see it as largely irrelevant for guitar playing. I've done full days in studios and not had to stop... if you wanna be bigger, that's cool, but I'm not sure it'll make a difference to your problem.

If the problem is postural, lifting weights ain't going to help. Regardless of the weights decision, I'd still go get yourself checked out by an experienced player / doctor or whatever - otherwise you could be in for more pain... On the off chance that you've actually injured yourself, the weights could make it way worse (hopefully unlikely).