Since you didn't say how physically active she was, my $0.02 is get her involved in something physical, like swimming, dance, volleyball, softball, basketball, etc. This will (hopefully) do 3 things. Get her to meet new people, potentially making new friends, 2) give her increased self esteem by participating in a sport, and 2) get her moving to help in the weight loss. Let her try several different ones if the first one doesn't seem to be her bag. At 5'7'' she could be a great volleyball or basketball player just waiting to blossom...maybe a longjumper...who knows
Good luck to the both of you, the things that some people have to endure at so young an age amaze me sometimes.