Ironically a 19hhPercheron may well have a lower weight limit than a good 15.2 cob, many heavy horses don't actually have the conformation to be good weight carriers plus their feet and joints are already carrying so much of their own weight that there's no excess capacity.
There's a catch 22 where a balanced sensitive rider can make it easier for a horse to carry them, particularly if it's their own horse that is doing far fewer hours than a school horse BUT you don't get to be that sort of rider without lessons. Also riding schools have to protect their horses since they usually have a significant workload and often at least some unskilled riders, hence the lower weight limit. And they're businesses, it makes no sense to keep a horse that isn't suitable for a wide range of riders.