It sounds like the daughter is jealous and feeling alone. It may feel to her that you're going to be "normal" and she won't. When you've been her fat-buddy for so long. Maybe you can walk together, exercise together, diet together, etc. Make sure she knows she's not alone, and that you'll still be struggling with your weight. It's not a magic solution and there is still work to be done. If you do it together, then it'll be easier for her to transition into a long term weight loss lifestyle. She's still young enough to learn how to do it right, and do it right now.
My daughter is only 10 years old, but already large. She's always been in the 90th percentile of height and weight, ever since she was born. She's not fat yet, but she can get there quickly. When I decided to have the surgery, we started walking in the morning, and I bought weights at home. She's been working out harder since I had the surgery, and is vowing to be healthy. She'll never be skinny, like many of her friends are. She's thick and always will be. But, what I'm trying to focus on right now is health. As long as I focus on that, she seems happier. She's proud when she makes good choices at school, and at Grandma's house (where it's REALLY hard to make good choices!)
I know one post said to not treat children as equals or to consult them. I didn't ask my daughter about the surgery, but I did talk to her about my fears and frustrations. I don't want her to go through the same denial that I did growing up. Fat mom, fat grandmother...etc. No one ever addressed a problem. So, I suppose it's how you go about it. You can confide in a child, but to a degree, and not lean on them for emotional support. I think that's the difference. I just think if my daughter sees my struggles, sees the heartbreak over my health problems now, she'll be able to make a better choice for her life during those moments when she is in charge. I'm not there all the time to tell her apples instead of cookies...so the more we communicate, the more strength she'll have to make that decision when I'm not around.