My gosh people are idiots! You are not too heavy to be riding a horse. If their horses couldn't carry your weight, I feel like there might be something wrong with their horses, ie out of shape, too long backed. Have you seen some of the guys that rope? Not only are they huge, the horse is carrying a heavy roping saddle and stopping a decent sized animal that doesn't want to be stopped.
I have ridden most of my life, at my heaviest, I was 234lbs, I rode a large mare with good bone, but that wasn't always the case. I never sored up a horse.
I am glad you found a barn and an instructor! Looking forward to hearing how it went!