I appreciate your concern for your friend’s weight, considering her eating disorder. But, she is at a healthy weight for her height if you are sure she actually weighs 120 pounds and is 5 feet 2 inches. You are 1″ taller than she and therefore can weigh more.
Actually, if a person weighs within their healthy body weight range, they should have a reduced risk for the major causes of illness in the U.S. (heart disease, stroke, cancer, diabetes). If a person’s weight falls below the lower range of healthy, then I would agree with you that their immune system would be negatively affected. People who live to be 100+ years of age are usually at the lower end of a healthy weight for their height.
Who has assessed your friend’s eating behaviors to determine that she has an eating disorder? Does she have a distorted body image or has she had wide fluctuations in her weight (+ or – 10 pounds within a couple of weeks)? Does she binge on a large amount of food then force herself to vomit? Perhaps, your friend needs to deal with her unhealthy eating behaviors which have not yet impacted her weight. Or is this your perspective given your past history with eating disorders?