At 11, he has entered a stage of development where being overweight gives him more emotional pain than it did when he was younger. Your focus needs to be as much on his emotional health as it is on his losing weight. Doing recreational activities with him that require physical activity would be helpful -- make fitness a pleasurable family activity. Getting help from a nutritionist who works with overweight kids would also be a good idea. Consult with an exercise physiologist who uses weight training as a means to get children's bodies more fit and strong.
I would honor your son's request for a different therapist. There are therapists who focus more on childhood depression and body image; make it your responsibility to find them by networking with your health care providers. Your son should be able to interview a therapist to see if he would be a good match. Make sure that any therapist or nutritionist works on his emotional needs, as well. Thanks for writing and keep me posted if you'd like.