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) with at least one of the following weight-related comorbidities:

1. hypertension: on blood pressure (BP)-lowering medication.
2. dyslipidemia: on lipid-lowering medication
3. cardiovascular (CV) disease: for example, ischemic CV disease, New York Heart Association (NYHA) Functional Classification Class 1 or II Heart Failure
4. obstructive sleep apnea
5. Have had a stable body weight for the 3 months prior to randomization (<5% body weight gain and/or loss).

Exclusion Criteria:

W8M-MC-OXA1:

1. Have any prior diagnosis of diabetes mellitus, that is type 2 diabetes mellitus (T2DM), or rare forms of diabetes mellitus, except gestational diabetes.
2. Have any of the following cardiovascular conditions within 6 months prior to screening:

1. acute myocardial infarction
2. cerebrovascular accident (stroke)
3. unstable angina, or
4. hospitalization due to congestive heart failure (CHF).
5. Have a history of acute or chronic pancreatitis.

1. Have a history of New York Heart Association (NYHA) Functional Classification I IV CHF.
2. 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.

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.

W8M-MC-CWMM:

1. Have a prior or planned surgical treatment for obesity, except prior liposuction or abdominoplasty, if performed >1 year prior to screening.
2. Have type 1 diabetes mellitus, latent autoimmune diabetes in adults, or history of ketoacidosis or hyperosmolar coma.
3. Have poorly controlled hypertension.
4. Have signs and symptoms of any liver disease other than nonalcoholic fatty liver disease.
5. Have any of the following cardiovascular conditions within 3 months prior to Screening:

1. acute myocardial infarction
2. cerebrovascular accident (stroke)
3. unstable angina, or
4. hospitalization due to congestive heart failure.
5. Have a history of symptomatic gallbladder disease within the past 2 years.
6. Have a lifetime history of suicide attempts.