The main purpose of this study is to learn about the safety and tolerability of LY3437943 when given to Chinese participants with overweight body mass index (BMI) or obesity. Blood tests will be performed to investigate how the body processes the study drug and how the study drug affects the body. Each enrolled participant will receive injections of LY3437943 or placebo given just under the skin. For each participant, the study will last about 20 weeks excluding screening period and may include up to 20 visits to the study center.

Inclusion Criteria:

For All Participants:

• Are native Chinese males or females
• Have a body mass index of ≥27 and ≤40 kilograms per square meter (kg/m²)
• Have not modified diet or adopted any nutritional lifestyle modification for 3 months
• Have stable body weight for the last three months
• Male participants must agree to use contraception during the study and for 4 months afterward and female participants must be woman of nonchildbearing potential

For Type 2 Diabetes Mellitus (T2DM) Participants:

• Have type 2 diabetes for at least 3 months
• Have a glycated hemoglobin (HbA1c) value of ≥7.0% and ≤10.5% and have been treated with diet and exercise alone or a stable dose of metformin for at least 3 months prior to screening

Exclusion Criteria:

For All Participants:

• Have an average weekly alcohol intake that exceeds 21 units per week (males) and 14 units per week and smoke more than 10 cigarettes, or cigarette equivalent (as determined by investigator), per day
• Have other serious or unstable illnesses
• Have had an episode of severe hypoglycemia
• Current or chronic history of liver disease.

For T2DM Participants:

• Have type 1 diabetes mellitus
• Have uncontrolled diabetes, defined as an episode of ketoacidosis or hyperosmolar state requiring hospitalization
• Any glucose-lowering medications other than metformin within 3 months prior to screening