Your friend should have no problem riding anything. I am 5'5 and probably weigh more than 350 and the only trouble I have had is some of the turnstiles, but the CM will let you through the chained area with no problem. DH and I didn't fit comfortably on Dumbo in the same car, but alone I would have been fine. Barnstormer was the same as Dumbo, I did okay with 10 year old cousin, until she decided she didn't want to ride, so I rode with Dh and it was tight, but not uncomfortable. The tea cups can be a bit tight, but no longer than you are on it, there will be no problem.
ALWAYS pull seat belts out before sitting down, because they are long enough. When Dh and I rode Dumbo, we had to use an extension, but if I had ridden alone, I probably wouldn't have needed it.
I don't go to other parks because of worries like this, but have never had a problem at WDW, It's my favorite place.
Suzanne