The purpose of this study is to evaluate how well LY4064912 is tolerated and what side effects may occur in healthy participants and participants with overweight and obesity - global. The study drug will be administered either subcutaneously (SC) (under the skin) or infusion intravenously (IV) (into a vein in the arm).

Blood tests will be performed to investigate how the body processes the study drug and how the study drug affects the body.

Inclusion Criteria:

• Age is 21-65 years old at Singapore Sites
• Participants who are overtly healthy as determined by medical evaluation including medical history, physical examination, laboratory tests, and cardiac monitoring

Part A: Body Mass Index (BMI) within the range greater than or equal to 21 and less than 30 kilogram per square meter (kg/m²)

Part B: a BMI greater than or equal to 27 and less than 45 kg/m²

Part C: a BMI greater than or equal to 21 and less than 35 kg/m²

• Parts A and C: Participants must weigh 60 kilograms (kg) or more at screening
• Have had a less than 5% change in body weight for 3 months before screening
• Safety laboratory tests are within normal reference range

Exclusion Criteria:

• Have a history or presence of cardiovascular, respiratory, hepatic, renal, gastrointestinal, endocrine, hematological, or neurological disorders capable of significantly altering the absorption, metabolism, or elimination of drugs; of constituting a risk when taking the investigational product; or of interfering with the interpretation of data
• Have history of diabetes (except gestational diabetes) or current diagnosis of diabetes (any form), or have HbA1c greater than or equal to 6.5% (48 millimole per mole (mmol/mol)) at screening
• Are individuals of childbearing potential (IOCBP).