I had some of the same concerns being a plus-size person as well.
I can speak for RCL that I never ran into any problems whatsoever, other than the bar stools in the casino and the sports bar as they're bolted into the floor so you cannot move them in or out. Not at the slots or tables, JUST the bar area. The seats in the Aurora Theater were large enough for me as well, which was surprising, but I had no problems and was able to enjoy the shows I attended.
We booked a Junior Suite which had the larger bathroom with tub. Now, this can be GOOD or BAD...I'm 37 and in good shape for being plus sized, BUT the tub is high off the ground, you kind of have to step in and then over the ledge. I had my hubby spot me to be on the safe side, both entering and exciting the shower/tub as it is quite a step down/up. Our friends were in an inside cabin (blech...
) and I would DEFINATELY not recommend that unless you want ALL your 'business' hanging out into your stateroom...I don't think a 150 lb person could take a shower in that bathroom!! Just being honest.
Now, my Mom is disabled and plus sized as well and she opts to go for one of the handicapped suites on the ship. They are not ALWAYS available but they have a larger bathroom, with wheelchair accessibility and a pull down bench to sit on. If you're not very mobile, this might be a better option for you (if available) and you'll get a bigger room for the same price.
The chairs in our Junior Suite and balcony were all very comfortable and no issues sitting on. Chairs in the formal dining room were fine as well. The chairs in the Windjammer had arms which were a little snug, but not horrible. They also have some tables with a bench on one side which is nice too. The chairs along the pool/windows were wooden on our ship and a little small, but not horrible.
The tender boats to port (which we only had one day in St. Thomas...) have VERY small seats but neither were jammed packed on our trips back and forth, and they are constantly running back and forth from the ship, so you don't feel guilty if you take up more than one seat (they are small...).
In summary, I would opt for a larger stateroom with tub OR if you're not very mobile, work with a travel agent to secure yourself a handicapped room. I never felt uncomfortable or judged or that there was no where to sit comfortably. The plane ride was the worst in my personal opinion....but, I don't think anyone likes the seats on planes, even if you're skinny
Have a wonderful time and have a wonderful Spring....