This study is researching an experimental drug called mibavademab. The study is focused on patients with a condition called monogenic obesity. Monogenic obesity is caused by a change in the leptin gene that keeps it from working properly. This causes the body to not be able to feel full or control feelings of hunger. The aim of the study is to see how well mibavademab controls the body weight and how safe it is. The study is looking at several other research questions, including: * How much mibavademab is in the blood at different times * Whether the body makes proteins called antibodies against mibavademab (which could stop mibavademab from working as well or could lead to side effects) * What side effects may happen from taking mibavademab