One of the best parts about horses is there is definitely a horse out there to suit you, and there are many people who are much taller and heavier than you riding daily and their horses are doing just fine. At 240 lbs, I was riding a 15.2, average-built QH gelding and a 14.2 QH/STB mare nearly daily with no ill effects to either.
Honestly, I wish the weight-carrying percentage “rule” would go the way of the dinosaurs because it breeds SO much misinformation, fear, and frankly makes people worry more than they should. Weight-carrying ability is not able to be reduced to a simple weight percentage in every situation- that’s patently crazy. That’s like saying a 600 lb man can carry 120 lbs all day because he weighs 600 lbs. In reality, that 600 lb man is morbidly obese and fighting his own body just to carry it around, and he’d be lucky if he could carry 5% more weight due to all the stress and strain on his muscles, joints, and organs. In the same way, a fit horse and an unfit, fat horse are going to carry weight very differently. You could feed a 1400 lb horse to 1600 lbs, but that just means he weighs 200 lbs more, not that he can carry that much more weight proportionally.
Also, height has very little to do with weight carrying. In fact, a tall horse with fine bone is going to have a harder time carrying a heavy rider than a short horse with thick bone, a short back, and a wide chest/barrel.
Take for example many of the “pony”-sized horses out there that carry full-size and yes, plus-size riders. Fell ponies, Haflingers, draft ponies, Gypsy Vanners, Icelandic horses, etc. All of these tend to be short with THICK bone- most rarely over 14 hands, but they are built for weight carrying because of their conformation because they are short, wide, and thickly built.
As for your trainer, I am willing to bet she is probably a very tiny person. I have found personally that very small people who do not weigh much have some truly wild ideas about what weight looks and feels like. To someone who weighs 100 lbs soaking wet, 200 lbs seems like an insane amount of weight.
You should strive for fitness with both yourself and your horse, but don’t stop riding simply because someone who didn’t have all the info told you that you couldn’t. One person is not the Gatekeeper of Horsedom, and thank God for that.