I am well above normal weight and still was able to fit into nearly everything I wanted to ride, including The Mummy, Ripsaw Falls, The Simpsons, Spider-Man, Jurassic Park...everything except FJ. One issue that can arise in this situation involves the unitary safety bar that comes down to restrain more than one person (e.g., The Simpsons). Because my size causes the bar to click into place fairly quickly, the other person/people in the ride car have a tougher time holding on for stability during the ride. I think this also occurs on Jurassic Park and maybe Spider-Man. I didn't get kicked off because of it, but it's possible the TM will come by and shove the bar down some more if they see riders not properly secured.
On a side note, Ripsaw Falls was a VERY dicey proposition. I did ride it, which turned out great because it was my niece's favorite ride, but it was quite a scrunch to get in there. The TMs probably should have kicked me out because I really wasn't properly seated in the ride car. Anyhoo, I'd suggest reading up on this particular ride for tips on how to fit when it comes back into service; I vaguely recall seeing a thread or threads about that.