Weight limits are generally somewhat arbitrary.

Take a 250 lb guy sitting on a 15 lb bike with 20 spokes in the front wheel. Half of his weight is going to be distributed over 6 top spokes of the front wheel, adding ~10 kgf to tension of each spoke. If these are thin bladed spokes, they are going to be preloaded to ~100 kgf and have another 200 kgf of reserve: weight of the rider obviously matters very little.

The real danger is that our guy is eventually going to hit a pothole, or jump a curb, and then, at the moment of impact, forces experienced by the wheel just might be strong enough to snap the spoke. Though these forces are still proportional to the weight of the rider, so a pothole that wouldn't pose any risk to a 150 lb rider would be damaging for a 250 lb rider.