I also became overweight at that same time. A lot of well meaning adults in my life made some pretty unkind remarks and put me on restrictive diets that were embarrassing in front of my friends. I wasn't comfortable with sports or good at them either. It became the start of a life long problem.
I think the important thing is to find something she will like. I always wanted to swim but I was not able to because no one would take me. I don't think it would be a very good thing to have her involved with anything that is competitive at all. That will only serve to deepen any emotional issues she already has over this. Just taking her swimming or finding some other thing she can do for herself would help so much.
Another great idea would be to start teaching her to cook. What if you picked up some cookbooks from weight watchers or some other very balanced type of eating plan. Make a habit of trying one new recipe every week and getting her involved in picking them up and making the food.
It's very possible that she may get a growth spurt very soon and grow up enough inches to thin out without actually losing any weight. That's what happened to me. I had about 3 good years that I wasn't not overweight. The problem is that people were so focussed on my weight that I still felt fat. Eventually I bloomed up to 180 by the time I was only 16. I lost it all when I was holding down full-time school and full-time work plus aerobic classes. But I never lost the emotional scars of being told that I was fat and not good at sports. My self esteem took so many hits. I am now in my 200's and have dieted pretty much for 20 years. I don't want to scare you more, but this is a crucial time if your going to help her through this without damage.
Suzi