The general rule is 20% of the horse's body weight (NOT 1/3!) - Texas even has a law stating so. BUT this can vary up or down - there are a LOT of things to consider - back, legs, rider ability and overall size being the most important.
Good, sound, well put together conformation will ALWAYS be able to stand up to more than a horse with faults such as being back at the knee, sickle hocked, post legged etc. Specifically with legs, you want to look at how much 'bone' a horse has - this is taken by measuring the circumference of the bone just below the knee. (apparant stockiness doesn't matter - this measurement does). BIG feet also make it much easier on the horse.
All this makes people believe drafts or draft crosses, due to their height and 'chunkiness' are the best weight carriers, which often isn't true due to other factors - drafts were usually bred to PULL a lot of weight, not to carry it, and therefore are conformed to fit that speciality. Their size also often counts against them: they have more of their OWN weight to support before they start with the riders'.
Likewise the back must be well put together with a strong loin coupling to carry more weight comfortably. A shorter back, also, is a great help. Deformities such as swayback or roachback will NOT help. A stocky horse with good legs will never be a weight carrier if they have a long weak back.
A lot depends on a rider. The old saying is that 'every pound on a beginner counts double'. An unbalanced rider who doesn't know how to carry themselves on a horse is going to be much harder to cart around, so while a horse may be able to carry up to, say 200lbs nornally, for a beginner that might only be 150lbs.
Generally, the best 'weight carriers' are well put together cobs, which I know are rare in the US but that's what we have here. Where I work the horses for larger riders are a 14.1hh and 15hh cobs.