Teens live in a pretty petty and vicious world, if the weight of one can be medically justified as dangerous and they or their consenting parents can afford for removing some excess weight, the option should be there for them. When it shouldn't be allowed is when it's somebody just being obsessive about having the "perfect" body and they don't really have a weight problem, we already have enough problems with "size 0" pants not only being a thing that actually exists but one people think you should be striving for.
I believe surgery should be an option for obese teens with the permission of their parents or guardians. Everyone has a right to decide what they want to do with their body. I think teens should be provided as much information about the positives and negatives of surgery before they choose the option but in the end I believe the decision should be up to them. If they believe getting surgery will benefit them then I think they should be able to make that choice.