Your daughter may have Cushing's syndrome, which can cause rapid weight gain and other physical abnormalities. This is because too much stress hormone cortisol is produced in the body. There are many ways to solve this problem, you can go to the doctor.
You say she eats well, but don't say what you consider "well" to be. What suits you might not suit her. And just because she doesn't seem to watch a lot of TV doesn't mean she's doing things that require physical activity. You also don't say if she's gained weight suddenly or it's been a slow process or if she has bobbed up and down as she ages. We're not all going to look the same -- in my family, for whatever reason, the females were heavy and got heavier with age and the males weren't. I have no idea why. In fact, my brother and my father and I were big eaters, and my Mom and my sister ate a lot less. Yet they got fat and we didn't. Different people can be quite different, in other words, and choices can be much more severe for some than for others.
That's hard because kids come in all sizes and varieties and it is ever changing! I swear my boys were wide, then thin and then wide and then thin as they shot up in height. There is a chance she is about to grow in height again very soon and this will even back out. When you say she eats well, what is her diet like? I have two sons, one who eats like a mother's dream and another that I have to manage. And my son has a friend who has always been heavy. His mom says he eats normal but in truth, what I notice is he eats larger quantities than other kids (my kids). We can order a pizza. My son a year older than him will have 4 pieces (he's a huge eater), my son this boys age will eat 2 pieces and the boy who eats more will eat 8 or more. And it is like that with everything. He's hungry a lot and eats a lot of calories in terms of portion size. Even if it is healthy food. His mom was told to limit calories when he too hit a level that the doctor became concerned. He's 5 foot 4 and weights 165 now. (at 12).
So, I'm curious about her portion size or any eating she may do that you are unaware of. I monitor our food (as the grocery shopper and provider) but some households are such that kids will have access that parents aren't aware of.
I know I try to not buy the snacky type food that temps us all.
And how is her physical activity?
Another question is her metabolism. Could you do any blood work on her to see her thyroid function? If she has a slow thyroid or is hypothyroid, it will result in more weight.
So, we'll go from there but mama to mama, I know it's hard. We'll help you!!