My family went 4 years ago and I'm 6' 2" and was also wearing 4x shirts. (for those that care, I'm still 6' 2" but I wear 2xl now and I'm working on getting down to a simple xl before our trip in November).
I was never turned away from any ride that I chose to ride. However, I did not go with my family on Space Mountain because I didn't want to squeeze into the cars and then have to wiggle my way back out after. I have a bad back and getting down into those little cars is not very easy.
Most of the rides (if I remember correctly) have simple lap belts. I know some of them have the bar that folds towards you but I "fit" in those. It was funny to ride with kids when you shared a bar because it held me down just fine, but it did nothing for the kid because my belly wouldn't allow it to close on them. I held on to them pretty tight, but they still had the lap belts.