Well my daughter went through this at about 15. I'm not sure my approach would work for others, but she was weighed by the doc when she had food poisoning and when I saw the weight I went nuts, I already knew she was too thin and we had discussed it, I asked her if she wanted to ruin her life by being an anorexic, with people staring in the street and pointing at her, looking freaky, being ill, her whole life focused on food , I was very angry she was doing this to herself, and then I ehrm grounded her till she put on weight, gave her a target, she was horrified, couldn't believe I was actually grounding her for this reason. She kept saying "you can't ground me". My response was "fucking watch me".
However it worked, she spent the next couple of weeks or so focusing on eating healthy and gaining weight and she's not reverted back and is now 19. She still watches what she eats and is still slim but she's a healthy weight and eats normally.
As said, it could make some kids worse, but for me it stopped what was clearly developing in its tracks. I think it was the talk more than the grounding, but we had reached the point where it had to be fixed or she really was going to ruin her life.
Each kid is different and uou would know you're own daughter, with mine I knew my strong intervention would work, for other kids it could make it worse. I'm not sure if that's helpful or not. I'm sorry.