Don't think the "larger" part of your question will matter, they have some big tubes and once in the water you are not going to be doing much of any work.. you basically just float down the river. The bad knees part is another story. To get to yoru launching point requires a hike through the jungle (on a jungle path) of about a 1/2 mile or so. (longer on some of the private excursion operators). This might be a big issue if you have bad knees. The path is wet and can be slippery and uneven.
I loved the cave tubing, but you may wish to reconsider.
We used Dennis at Explore Belize Caves back in November, and were very pleased with the service. There were 22 of us on a private tour we set up, we had 3 tour guides. They could accomodate any size person, we even had a gentleman that was and ex football player, weighing in at around 365 pounds, and he had a great time. And yes, butts up is a great saying..you learn real fast what that means when you are floating through the caves.
Since all the tours are practically the same (they all go to the same place in the river) you'll be better off with a small group that Reggie has to offer. If he gets more people signed up for a particular day he has a bus to accommodate everyone. It's much easier to navigate with only 6 or 8 people in a group rather than 40 with the ship tours. If you make reservations online with Reggie, he'll be at the waiting place he will wait until you arrive. We even took on an extra 2 people along the route from another tour operator who only had two people going- They seem to work with each other. Another plus in going with Reggie is that he'll drop you off for shopping anywhere in town on the return leg and his price is probably 2/3 that of the ship's tour.