Suppose it depends if you are talking horses or ponies. Highland ponies for example are capable of taking a lot of weight. A chunky cob or welsh sec d are also strong & can be weight carriers. As for horses it all depends on the stamp of horse, my tb is a steeple chaser build, he's well capable of carrying a man, as would be many other breeds or mix breeds depending on how they are built & put together. It's a question that has a lot of answers.
Haflingers and highlands are renowned weight carriers but I wouldn't want 16st on my haffy for regular hard work like jumping and hunting etc and she is quite a large example of the breed. I wouldn't mind if it were the odd hack, I am quite heavy myself I just think that would be a stone or two too much. Highlands are obviously meant to carry a stag but I doubt that ever involved jumping or much galloping.
I guess the more substantial cobs 15.2hh plus would cope with it easily or IDs and chunky cob x ISH types.
Suffolk or Percheron, shire or Clyde for that type of weight. Although if the horse isn't fit and so it's back isn't strong, no breed will be suitable for that type of weight.
My Westphalian Draft horse (looks like a 16hh Ardennes) has carried an 18st absolute beginner quite happily for 20/30 mins. She is very short-coupled for her girth and far more capable of carrying this weight than my 16.3hh chunky ID with a long back was. I would think that she could carry up to 16st capable rider on a reasonably long hack, with a few logs to get over, quite happily. She doesn't really do jumping, preferring to use her weight to destroy anything in her way, so wouldn't be much good for hunting etc.
ETA, if you decide to go down that route do be careful about where you buy from.