I think I would tell her Mum.
Unfortunately, you will probably lose your friend, hopefully temporarily. However, which would you prefer, a temporary glich in a friendship or constant worry and probably a lot of arguments with her? I think I would also tell her that I was going to tell her Mum. It saves endless worries and secrecy about 'who told on me ?' etc.
Her Mum probably already suspects that this is going on, hence the feeding up and the worry.
Just to add to your woes, don't be surprised if her Mum is annoyed with you at first too....when it's bad news, the messenger usually gets the blame.
On the bright side, your friend has almost certainly been doing this for a year or so from what you say of her weight loss.If she's managed to keep it to herself for so long, it may be no accident that you found out. She may have reached the point where she wants someone to help her and/or get her to the help that she needs.
Good Luck and well done you for being such a concerned , good friend.