If it was the only way to get my kid to lose weight, I would pay my kid to lose weight

I think that would probably be a big mistake, since the kid would be most likely take the most quickly discernible path to weight loss, i.e. a calorie reduction diet, which I think is a very destructive way to lose weight. Go for the quick fix, eat half as much for the next month, lose the ten pounds, collect the hundred dollars, then go off the diet, and watch fifteen pounds pile on over the next two weeks. It's a very effective way to change your set point and gain weight. I know, I've tried it. In my case it wasn't for reward money; it was to escape the nastiness and criticism I had brought upon myself for daring to gain curves during puberty. Nice job, mom.