I think it's really nice that you would ask. Good for you! It's nice to see someone think about the horse first.
Remember, these figures are with the weight of the saddle and saddle blankets - that can add up to 30 lbs itself, depending on saddle type.
The 20% (1/5) was from the cavalry, originally, and they didn't much care if the horse survived the experience or not. So I stick with that unbearably annoying horseman's prerogative, 'It depends'.
I generally stick to the 20% rule - if I make any adjustment to it, it's to LOWER the weight of rider allowed. Meaning not over 20% regardless.
Meaning, ok, the horse is 1500 lbs, but has a weak back. He should have LESS than a 300 lb rider. The work is going to be fast? Then the weight of the rider allowed, goes DOWN. He needs a LIGHTER rider than 300 lb. More hours in the saddle? Again, rider weight needs to be LESS. Etc.
That says a 200 lb man can ride a 1000 lb horse. Or a 300 lb man can ride a 1500 lb horse. A 1000 lb horse might be a modern Quarter Horse or a taller Thoroughbred horse. A 1500 lb horse is most likely, a very sturdy draft horse cross.
It's not just the weight of the horse that makes a horse 'up to weight'. The actual bones and joints of the legs should be large and sturdy. The back should be muscular and strongly built (not dipping down). The horse needs a generally good build, with large hind quarters and all the right angles in each part of the legs.
I COULD have a 1500 lb horse that I'd avoid putting a 300 lb man on, if the horse's back or hind legs looked weak, or it had other faults. I might keep a heavier person off an old horse, or one that was having a problem with leg pain.
It's not always 100% about height, either. There are, rarely, draft crosses that are 15 or 14.3 hands, that are really, really massive all over, and just aren't very tall. They MIGHT be up to more weight, depending on just how they're built. But quite often, these horses have other faults in how they're built that DROPS the amount of weight they should carry back down to what their height indicates. Long weak back, narrow, small hind quarters that trail out behind them when they move, etc.
SOME of it could depend on HOW the rider is big. If he was 5'6'' and had a huge amount of weight in a big heavy belly, he'd be able to 'carry' that and control it much less well on a horse, than the guy who's just very fit, muscular and powerful all over, and has a slim belly. Fat is uncontrollable weight, muscle is controllable weight.
SOME of it could depend on how experienced the person is. I MIGHT want a beginner on a really solid, sturdy horse even if the beginner was fairly light.
Then there's what you plan on doing.
Top speed = rider's weight is 10%
A jockey is usually about 100 lbs on a 1000-1200 lb horse. That's closer to 10% of the horse's weight. That to me says, that you can start at 20% for pleasure riding, brief, easy rides, and then start whittling away at what's ok as you get into more and more vigorous and demanding riding.
Going to a more demanding type of riding, eventing ('3 day') riders that do dressage, run cross country and show jump, usually look like very lean, trim athletes. They usually run and do other sports in addition to riding to keep trim. They even lobbied to have a MINIMUM weight rule for the rider removed, and that minimum was 165 lbs. They showed from research, that jumping with more weight on the horse, makes a significant difference in the strain on the horse.
Moderate speed and/or difficulty - rider's weight 15%
Pleasure riding - brief rides on easy trails or in the ring, no jumping, advanced movements = rider's weight 20%
And you'll hear a ton of argument about this. A lot of people don't follow the above guidelines and they get mad when someone blurts 'em out.
So, what do you want to do? Ride casually around the farm once in a while on a borrowed horse? Or gallop and jump several times a week, raising those jumps higher as time passes and increasing the gallop speed? Ride endurance, spending many hours a day in the saddle? If you want to do something more stenuous, consider a lower weight limit.
I don't see the 'big huge heavy man on the tiny reining horse' as a justification for putting a big heavy man on a small horse. I don't think they're doing any thing in the best interest of the horse, especially not for reining. And most of those guys are the worst kind of 'big' - a big uncontrollable belly. I watched one of the top reining trainers in the WORLD almost fall off a horse when he lost his stirrup in the World Equestrian Games this year and almost throw his horse down to the ground. Great big belly on the man. It just is not 'controllable weight'.