Drafts and draft crosses are actually worse weight carriers due to their conformation (bred for pulling, not being ridden) than short, stocky horses. Your old-school Morgans, Haflingers, Fjords, Welsh Cobs, foundation QH types can easily carry a competent 200+ lb rider.

Person 1)QH or paint
Person 2)Off-track Standardbred. Unflappable.