Yep. What
@Vertigo said. They're fine for carrying or pulling heavy weights, just not built for speed and agility.
Heavier riders tend to try to find heavier horses to carry them in the belief that they'll do less harm to a heavy horse, but there's more to it than a simple weight-for-weight comparison. Many heavy horses are just heavy in the body, with legs too finely-built in relation to the weight they carry, whereas a horse such as a Shire has massive tree trunk legs that can easily carry a heavy human (with or without armour) in addition to their own fat bellies. As always, it's a compromise between weight-carrying ability vs agility in battle, stamina, speed, etc.
Back in the day, my uncles were all miners who handled pit-ponies. Those wee critters hauled heavy loads and often carried grown men on their backs. However, in those days humans weren't, as a rule, so careful of the feelings of their beasts of burden. They might have been aware of the financial cost of a lame or sore pony, but there'd have been little empathy for the pony's feelings. Think of how they treated their fellow human beings in the slave-trading years and it's easy to see that the concept of cruelty to animals would have been something they'd have laughed off.
In modern times, the swing is perhaps too far in the opposite direction. There's nothing wrong with, say, a full-sized adult riding a pony (within reason), as long as the pony isn't being asked to go fast, jump, or cover difficult terrain. Heavier riders often come under fire for riding at all, however carefully they choose their mount. There's also a big difference between a good, experienced rider, who balances well and moves smoothly with the horse's movements and an bad or inexperienced rider who rides like a sack of potatoes, bouncing around on the horse's back and losing their balance.
