This NY Times article about eating disorders among Orthodox Jews raises some theories about the origins of eating disorders in this population, but I think there are some other possibilities.
Modesty may make it harder to dress well for women who are even slightly overweight. Thin women look fine in a wide range of clothes, but slightly overweight women need to be creative in ways that don't always work with modesty restrictions --- showing cleavage is a good way for men not to notice extra fat elsewhere.
Also I suspect that being sexually involved is helpful for overweight women and their partners to feel good about their bodies. For religious women, that reinforcement isn't available. Religious men who have no experience either way may assume that thin women are better in bed. Alternatively, thin partners are more socially valued, and the social value may bring gratification pre-marriage. Likewise, religious women cannot feel sexy or sexually empowered by sexual activity. They may feel sexually empowered about how thin their bodies are, so they may seek thinness as their primary form of feeling sexy.
Because these alternative outlets for feeling desirable are not available to Orthodox teens, they need to find other ways of feeling good about themselves. I wonder whether the types of exercise that are incompatible with anorexia, such as weight lifting where it's important to eat minimum amounts of protein (0.5-1 g protein per pound of body weight) and to be moderate in quantity of exercise (every other day, at most), would be helpful. Gymnastics, dancing, rock climbing, and other ways of using that strength could also be helpful in helping teen women feel confident about their bodies, and also staying healthy.
Meanwhile, teen males also need to change their attitudes and how they perceive women of different sizes. That's harder, especially if they do not interact much with the opposite sex.