This is a 4-part study that includes a Part A, Part B, Part C, and Part D. Parts A and D will study the safety and tolerability of the study drug known as LY3537031 in participants who are overweight and obese. Part B and Part C will study the safety and tolerability of LY3537031 in healthy participants. Part C will contain only Japanese and Chinese healthy participants. Blood tests will be performed to check how much LY3537031 gets into the bloodstream and how long it takes the body to eliminate it. Body weight will be measured. The study will last approximately 49 weeks excluding a screening period.