Most people I know who are over weight are concious of this fact and tend to feel bad if asked to ride anything that they feel can't support them.
Of course you do find people who consider horses machines and think that since the animal weighs so much, it should be able to cart them around. This could be a sense of denial on her part.
"I can ride, I cut sugar from my diet"
Well, honey...not to offend, but sugar simply isn't enough if you want to drop a large amount of weight.
At the weight she is now, it not only poses a threat to the horse's health, it poses a threat to her own health. If she is that extremely overweight, she doesn't have the muscling to keep herself on the horse if the horse would do anything spontanious. Good rider or not, you need muscle if you want to sit a rollback/bolt or anything else a horse can do that's out of rythm. I knew a woman who was so grossy overweight that when the horse turned sharply on it's haunches, she just plopped right off. She had to cast her arm with pins and slings and whatnot.
Its not just about weight loss, its about muscle gain. It just won't hurt the horse, it has the potential to hurt the girl. Good for you for putting your foot down and not buckling when she wants to ride. It will keep both parties equally as safe.
And those who were seen dancing were thought to be insane by those who could not hear the music