The description provided indicates behaviors that are characteristic of bulimia nervosa. Peggy engages in binge eating followed by self-induced vomiting and is fearful of gaining weight, which aligns with bulimia. The fact that she has an average to above-average body mass index does suggest that she may not meet the diagnostic criteria for anorexia nervosa, which typically includes underweight status.
Therefore, the best answer is:
Only bulimia fits this description.