If I could give any piece of advice, I think it would have to be...
DON'T WORRY ABOUT IT!
I know, I know. It's so much easier said than done. But really, WDW is a wonderful place that is very accommodating. I'm 5'9", and... well, let's stick to saying I'm a size 26.
My grandmother is 5'7", and around 330 pounds. My uncle is gosh... Probably 6', and a good 400lbs, if not more.
The teacups can be a problem. I went on with my "niece" one year, who was about 7 at the time. For me, it was all about my knees and I was very uncomfortable, but for her, I would do it all over again

(My best memory from that trip is skipping with her from Peter Pan to the teacups

)
My uncle is a big fan of ToT and EE. RnR is a bit hard on his back, but if his back was better, he would probably still be going on that too!!
My grandmother and I always sit next to each other. The only exception to this has been Kali River Rapids in Animal Kingdom. We absolutely cannot sit next to each other on that, so we request that we each have a separate seat. (The way it is set up is that, there are several (maybe 5 or 6) sets of seats - each set seating two.)
Other than that, we always do everything together, whether it be BTMRR, PoTC, SplMtn, PP, WtP, IASW, HM... She won't go on Space though. That is a very, very tricky ride to maneuver out of. I request seat 1 or 4. TI've sat in the others, but they are very uncomfortable with my knees. At least with 1 or 4, my knees are able to be more "free". The CM is usually extremely kind about it, and will just say "please wait for one moment".
As for Epcot... I think the most worrysome ride is Mission: Space. It can get awfully tight. She went on it once, and felt very claustrophobic. We weren't able to be together then, because she was in a
scooter. She hasn't been on it since, even with the non-spinny version being in place. We can both sit two to a seat on Spaceship Earth with no problem, sit together on Soarin... I think the only thing that was remotely uncomfortable were the seats at Impressions de France, but that is a little fuzzy to me. Overall, Epcot is an A+ on the "Plus size" factor in my book. (I never went to Epcot with my uncle)
DHS.. My grandmother used to love ToT, but once they added the "It's-totally-random-how-many-times-you-fall" thrill and we were dropped 6 times, she isn't a big fan anymore. My uncle loves it, and we had no problems sitting together. I haven't been to TSM yet to speak of anything there. If I recall correctly, it felt like the Little Mermaid show had seats a little low, so that was fun getting out. Sounds Dangerous and The Muppets have tight seats, but it's all in the maneuvering. At DHS, my grandmother loves Star Tours, and would probably ride it all day if she could
DAK... The biggest obstacle is KRR, IMO. And btw, my uncle LOVES EE.

I remember the first time I went on it, I caught him going on... for the fourth time in a row (during evening EMH)
I'm sure by now the CMs understand, so don't be afraid. I know, like I said, it's easier said than done but Disney has definitely planned, and strives so hard to not turn anyone away due to their weight, disability, or anything else. So try not to worry about it and have the time of your life with the mouse! I wish I could be there too!!!