Part A is a Randomized, placebo-controlled 36-week study. Part B is an Optional open-label 52-week study. There will also be an optional Reward Sub-study, including healthy controls, designed to investigate leptin's relation to reward processing by collecting participants' brain and behavioral responses to images (e.g., pictures of food vs. non-food). Brain responses will be collected and will also be assessed via functional Magnetic Resonance Imaging (fMRI).