A Study of LY3305677 Compared With Placebo in Adult Participants With Obesity or Overweight

Inclusion Criteria: W8M-MC-OXA1: * Are males and females who agree to abide by the reproductive and contraceptive requirements W8M-MC-CWMM: * Have a BMI ≥27 kilograms per square meter (kg/m²) Exclusion Criteria: W8M-MC-OXA1: * Have any prior diagnosis of diabetes mellitus, that is type 2 diabetes mellitus (T2DM), or rare forms of diabetes mellitus, except gestational diabetes. * Have any of the following cardiovascular conditions within 6 months prior to screening: * acute myocardial infarction * cerebrovascular accident (stroke) * unstable angina, or * hospitalization due to congestive heart failure (CHF). * Have a history of New York Heart Association (NYHA) Functional Classification I-IV CHF. * Participants with hypertension who do not have well-controlled blood pressure (BP) (\>140/90 mmHg), regardless of antihypertensive treatment. Participants receiving treatment for hypertension should be on a stable antihypertensive regimen for at least 3 months prior to screening. * Have a history of acute or chronic pancreatitis. Note: If the investigator anticipates a need to add antihypertensive medication during the study, the participant should not be included in the ambulatory blood pressure monitoring (ABPM) procedures. CWMM: * Have a prior or planned surgical treatment for obesity, except prior liposuction or abdominoplasty, if performed \>1 year prior to screening. * Have type 1 diabetes mellitus, latent autoimmune diabetes in adults, or history of ketoaci…