A heavy person whose weight is largely bone & muscle is more likely to balance well. There are enough challenges in balancing on a horse - at least for those of us who started later in life - without fighting extra weight as well. If I had to put on the battle gear I wore in Afghanistan while riding, it wouldn't be just my horse who would complain!
But that doesn't mean someone cannot ride. The back injury I received with Mia's help in Jan 2009 probably did more harm to my balance and ability to move with the horse than an extra 50 or 75 lbs of weight would.
If you have a physical limitation - be it a fat belly or a rigid back - you may need to make some compromises in your riding. No jumping, for example, or no starting a green horse who doesn't know how to balance a person's weight. It may mean you need to use a western saddle to distribute the weight over a larger area, or limit your rides to 30 or 45 minutes instead of 3 hours. It may well mean using a mounting block, or selecting a horse with thick loins and thick legs. It may mean taking lessons, and taking those lessons seriously.
But with some adjustments, you can still ride. And riding often gives one the incentive to lose weight, or to work on getting your back more flexible. It can also help create a positive attitude toward life, and that often helps with weight. I doubt I'm the only one on this forum who, after having a rough day, has saddled up his horse and ridden her largely to relax. I've even told her, while saddling up, "We're not going anywhere particular this evening...I just want the pleasure of your company." And being the supremely egotistical mare that she is, she seems to understand - after all, who wouldn't
want her company?
I've seen a 100 lb girl bounce so much that the horse pinned its ears, and shortly after that refused to canter or go any faster than a slow trot. With some skill, a good saddle, a fit horse, and an appropriate agenda for the ride, a person can reasonably ride up to about 30% of the horse's weight. But it is important, as the load increases, to have some control measures to care for the horse. They are forgiving creatures, but we need to make sure we don't give them too much to forgive...