A horse can carry about 25% of its weight while doing strenuous work and not have any major problems (most Thoroughbreds will average around 1100 lbs so that would be a max of 275 lb rider, a range your son is well within) . I, too, suggest looking into perhaps a Thoroughbred/Warmblood cross or a nicely proportioned Thoroughbred/Draft. There are some really lovely ones out there. I'm also very partial to Irish Sport Horses and I think they are fabulous jumpers. Don't discount a horse due to breed though. Look for something that's got good thickness of bone and look at overall proportions and build. There are TONS of thicker built, tall-ish Thoroughbreds out there.
Also, while I know it's not hunter/jumpers, William Fox-Pitt (a very, very successful British eventer and one of the top eventers in the world currently) is about 6'6" and is commonly seen riding horses in the 16.0 hh-16.1 hh range. He's pretty long and lanky, but that's still a bit man on an average size horse and he looks fine. It's also about how effortless the rider makes it look! If you're just clunking around like a sack of potatoes up in the saddle than any size rider can look bad on any size horse.
"Always be yourself. Unless you can be a unicorn. Then, always be a unicorn."