The purpose of this study is to evaluate the effects of a once daily subcutaneous (SC) injection of RM-493, in subjects with POMC (propiomelanocortin) or other related rare genetic mutations, on body weight, metabolic function and blood pressure. Patients who respond during the initial 84 days of treatment can enter into long-term (2-year) extensions. The study drug (RM-493) will be administered in an unblinded fashion.