I feel that this situation is nowhere near as simple as labelling it as 'abuse' and looking at 'punishment'.
There are clearly deep-seated psychological issues at work here for parents and the girl involved, which feed - if you'll pardon the pun - on each other.
I believe this behaviour can only be seen as a crime when a law has been broken, or a genuine social tabboo crossed, and I don't believe either is the case here.
As a society, we tend to adopt an unsympathetic view towards obesity, tending towards a self-blame and lack of control, neither or which adreess the problems. These attitudes in turn stem from our fundamental dislike and distrust of obese people, which tends to increase their issues, rather than address them.
So no, help and a little empathy rather contempt or punishment are what is needed here