3 ideas:
1. You could do what my parents did. Involuntarily enlist her in a sport every season, and then swim boot camp every summer. I never lost my blocky shape as a kid, and at the time I really disliked most of it. But in college, when a lot of people like me just became sedentary and even heavier, I was outside playing. Those sports never made me a hardcore athlete but they gave me a diverse range of interests and the muscles necessary to try new things (and also the lack of fear of pain necessary to try). So believe me, I was ungrateful at the time but I would have significant health issues today if they hadn't done so.
2. Develop outdoor hobbies as a family. This is the option I'd choose. Some neighbors did this. Go bike riding every weekend. The neighbors used to take us on 5-10 mile bike rides Go hiking. It would help your other kids burn energy. Sign up for kid friendly fun runs (maybe Disney
). Take family golf lessons or skiing lessons or something. Sign up for rock climbing lessons. Take up yoga or zumba and take her along. This way she won't feel like she's the target and staying active is the real struggle. I mean you're concerned about her weight, I get it, but at this point in my life I've been all kinds of weights and the best kind is healthy. As in I have been skinny and unhealthy and sedentary as well as heavy and healthy and active and the latter is vastly preferable. The key is to expose her to as many alternative activities as possible that she might develop and interest in and maintain as an adult. Someone who isn't interested in volleyball might love dance. Someone who isn't interested in track might love trail running or zombie and paint marathons.
3. This should be in combination with the other two. But get her interested in cooking and knowledge about food. My mother taught me to cook but it didn't stick because she only taught me how to cook her favorite dishes- stuff I mainly can't eat now and nothing that excited me. See if there's anyone who teaches pastry classes or Asian cooking classes or anything like that in your area. Have her start a Pinterest board of ethnic recipes she'd like to try. Maybe get her to plan a few meals a month for your family. Take her to fancy kitchen stores- maybe add to your cookware collection. Tools that intrigue her, pretty pans that might make her excited to cook. Make the focus cooking from scratch and whole foods and farmers market. When she learns that stuff tastes way better than 90% of restaurants or ready made foods, you've nearly won the war.
Seriously. I can't emphasize this enough. If you told me I couldn't have junk food because it was unhealthy, I would have tried to live on it (which is exactly what happened as a teen). I learned in college that carrots could taste better than candy, that farmers markets were worth getting up at 6 for, that organic meat made a difference, and that quality was better than quanitity.
(And now my parents are simultaneously delighted that I come home and cook but bemused by my "exotic" food choices and grocery bill. So I suppose the danger is that she'll be dragging you to oyster bars on vacation rather than fish and chips but hey, at least u won't be worried about her weight anymore lol.)