I just want to mention here how carefully you need to tread around this issue. Most young girls are extremely conscious of their bodies and doing or saying anything that makes her feel "fat" could lead to a serious eating disorder. Trust me I have been there. If she continues to gain weight even though she is active and you have taken the junk food mostly out of the picture (I wouldn't remove it completely unless you say that YOU are trying to eat healthier and it helps not to have it in the house) I would take her to the doctor for some blood tests. There could be a thyroid or metabolism issue that needs to be checked out.

That's good point Rose.  By accompanying her in doing exercises or other outdoor activities, you will get the benefits of the activities yourself. Is it hard to ask her take more vegetables and fruits?

I think the real cause is obvious: she eating a lot. Yes she is pretty active, but what kind of activities does she usually do? Mental activities wouldn't burn your calorie so much.

I would get her a check up with the doctor to be sure everything is okay. My suggestion to get her moving more would be to go for walks together. My kids love walking with me.

How old is your daughter? She might be having a slow metabolism and that is the cause that she is gaining weight. Go to a doctor for a check up to determine the real cause why she is gaining weight.