A Study of Brenipatide (LY3537031) in Healthy Participants With Overweight or Obesity

Inclusion Criteria: * Are overtly healthy with no comorbidities related to body mass index (BMI), such as type 2 diabetes mellitus or unstable cardiovascular disease, as determined by medical evaluation * Have a BMI within the range of 27.0 to 45.0 kilogram per square meter (kg/m\^2) * Have no significant (not more than 5 percent \[%\]) self-reported weight gain or loss in the past 3 months prior to screening Exclusion Criteria: * Have significant history or presence of cardiovascular, respiratory, hepatic, renal, gastrointestinal (GI), endocrine, hematological, dermatological, or neurological disorders capable of significantly altering the absorption, metabolism, or elimination; constituting a risk when taking the Investigational Medical Product (IMP); or interfering with the interpretation of data * Have a prior diagnosis of type 1 or type 2 diabetes mellitus * Have a history of acute or chronic pancreatitis * Have a personal or family history of medullary thyroid carcinoma or have multiple endocrine neoplasia syndrome type 2 * Have received a glucagon-like peptide-1 (GLP-1) receptor agonist, glucose-dependent insulinotropic polypeptide (GIP)/GLP-1 receptor agonist, GIP/GLP-1/glucagon receptor agonist, or amylin receptor agonist within 6 months prior to screening * Have been treated with prescription and over-the-counter medications, or alternative remedies (including herbal/nutritional supplements), that promote weight loss within 6 months prior to screening * Are pregnant or lactating