They can still suffer from anorexia and bulimia. You don't have to be super skinny to have those disorders.
Anorexia nervosa is a psychiatric diagnosis that describes an eating disorder, characterized by low body weight and body image distortion, with an obsessive fear of gaining weight.
I know it says "low body weight" there, but notice how it also mentions "body image distortion" and "obsessive fear of gaining weight".
Bulimia nervosa is an eating disorder characterized by recurrent binge eating, followed by compensatory behaviors, referred to as "purging". The most common form—practiced more than 75% of people with bulimia nervosa—is self-induced vomiting; fasting, the use of laxatives, enemas, diuretics, and over exercising are also common.