The main purpose of this study is to determine the effect of LY3437943 when administered subcutaneously on the levels of combined oral contraceptive (COC) ethinyl estradiol and drospirenone in the blood stream in postmenopausal female participants who are overweight or obese. The safety and tolerability of LY3437943 when administered with COC will also be evaluated. This study will last up to approximately 29 weeks for each participant.

Inclusion Criteria:

• Postmenopausal female participants
• Body mass index (BMI) within the range 27.0 to 40.0 kilograms per meter squared (kg/m²)

Exclusion Criteria:

• Have an unstable disease or a disease constituting a risk when taking the study intervention.
• Have significant renal insufficiency
• Have an important gastro-esophageal reflux disease, pyloric stenosis, gastroparesis or a history of gastric bypass surgery.
• Have a history or presence of chronic or idiopathic acute pancreatitis.
• Have a history of severe clinically significant multiple or severe drug allergies.
• Have a personal or family history of medullary thyroid carcinoma or have multiple endocrine neoplasia syndrome type 2
• Have had any malignancy within the past 5 years except for basal cell or squamous epithelial carcinomas of the skin or in situ carcinoma of the cervix that have been resected with no evidence of metastatic disease for 3 years
• Have any form of diabetes mellitus other than type 2
• Have type 2 diabetes with HbA1c greater than or equal to 10% at screening
• Have received an oral or transdermal patch hormone replacement therapy (HRT) within the last 1 month prior to screening or depot injectable HRT within the last 6 months
• Have received any investigational drug within the last month or 5 half-lives of this drug, whichever is longer, prior to screening. If the half-life of the previous investigational drug is unknown, the washout period should be at least 3 months before screening
• Show evidence of HIV infection or positive HIV antibodies
• Have evidence of, or test positive for, anti-hepatitis C virus antibody unless a confirmatory test for hepatitis C virus RNA is negative
• Test positive for hepatitis B surface antigen. In case a hepatitis B virus DNA test was also performed recently and is positive, the participant should be excluded independently of the hepatitis B surface antigen test result. The hepatitis B core antibody test is not used to assess eligibility
• Have acute or chronic hepatitis, or signs and symptoms of any other liver disease, or with significant abnormalities in laboratory liver tests
• Have a fasting triglyceride level greater than 500 mg/dL at screening
• Used any nicotine product including tobacco or nicotine replacement products within 1 month prior to screening or a positive cotinine test at screening. Are unable or unwilling to refrain from using such products during the study
• Have donated at least 450 mL of blood within 8 weeks before screening or intend to donate blood during the study