It may not have been the biggest limiting factor but if he has less bad weight it will help everything. You can get to your spots with a little more speed it can improve your decision making in that you have more options or more clean passing lanes. May not help the jumper a ton but shooting starts with legs and having less strain there may help with consistency of mechanics... its a bit of a stretch but it can't hurt.
Meh...his weight is not even in the top 5 things I think he needs to work on. His body and athleticism are the only things keeping him in the league in the first place. Yeah, he's a bigger dude but I think people are just obsessed with calling NBA players fat/lazy whenever they can. Seems a little weird to focus on that stuff when his shooting/decision making is so poor. If he can develop just one or the other, he will likely be a long term player in this league. Of course he can get into better shape, almost every player can, but a little skill development would go a lot further than him getting in picture perfect shape. Getting to that point where he can either 1) be a reliable ball handler/decision maker or 2) good enough shooter where he can play off the ball is paramount. Can't think of a single time where a player had a major skill development and his weight loss was ever considered as a key factor in that development, so yeah I'd say it's a stretch.