Just being heavy is less of a concern if most of the weight is in muscle bulk... More of a concern if it is mostly fat.
There's a few reasons... The first being without the appropriate muscle bulk you won't have the body strength to jump properly, and jumping improperly (At any weight) is unsafe for both horse and rider. The second being it becomes very challenging to get correct position and balance the heavier you are. Third, your endurance becomes taxed at higher weights, as exhaustion sets in your horse will have to work even harder to compensate.
The general rule is the rider, with all tack and outerwear, should not exceed 20% of the horse's body weight. For jumping, any height, I might even be concerned about that much if the rider is not EXCELLENTLY balanced. I have seen wrecks from unfit, overweight people jumping and causing the horse to come off balance because they felt it unfair to be excluded simply because they were heavy (granted I would say that in each case it was a rider who I would consider "morbidly obese" as opposed to "plus sized" )
The heavier the rider the more important saddle fit is too!