The purpose of this study is to measure side effects of LY3971297 injection administered under the skin in healthy participants and obese participants with high blood pressure (BP). Blood tests will be performed to check how much LY3971297 gets into the bloodstream and how long it takes the body to eliminate it. This is a 7-part study. The study duration will be approximately 60 days for Parts A and F, and approximately 90 days for Parts B, C, D, E, and G.

Inclusion Criteria:

• For Parts A, B, C, E, and F: Overtly healthy males or females as determined by medical history and physical examination
• For Parts A, B, C, E, and F: Have a screening body mass index (BMI) in the range of 18.5 to 35 kilogram per square meter (kg/m²), inclusive, with no significant weight gain or loss in the past 3 months prior to screening
• For Part C, to qualify as Chinese for the purpose of this study, all the participants' biological grandparents must be of exclusive Chinese descent and born in China
• For Part D, participants must have a stable dose of medications within the past 3 months prior to screening
• For Part D, obesity BMI in the range of 30 to 40 kg/m², inclusive, with a waist circumference of at least 102 centimeter (cm) for men and at least 89 cm for women for participants of US sites only. For participants of Singaporean, South Asian, Japanese, and/or Chinese Origin at sites outside the US, the BMI range is 27 to 40 kg/m2 and the waist circumference is at least 90 cm for men and at least 80 cm for women
• For Part E, to qualify as a participant of the first-generation Japanese origin, the participant, the participant's biological parents, and all of the participants' biological grandparents must be of exclusive Japanese descent and born in Japan
• Male participants must agree to adhere to contraception restrictions and female participants must be women not of childbearing potential
• For Part G, have a screening BMI in the range of 18.5 to 40 kg/m², inclusive, with no significant weight gain or loss in the past 3 months prior to screening
• For Part G, participants have a decreased estimated glomerular filtration rate (eGFR)
• For Parts D and G, participants are allowed to have stable background treatment for hypertension, type 2 diabetes mellitus (on oral drug therapy and/or long-acting insulin), dyslipidemia (on statin therapy) and/or hypothyroidism as determined by the investigator
• For Part G, Participants should be on a stable dose of angiotensin converting enzyme inhibitor or angiotensin II receptor blocker

Exclusion Criteria:

• Have a history of or current cardiovascular, respiratory, hepatic, renal, gastrointestinal, endocrine, hematological, or neurological disorders
• Have known or ongoing psychiatric disorders that, in the opinion of the investigator, increases the risks associated with study participation
• Have blood pressure and/or pulse rate constituting a risk as determined by the investigator
• Have a systolic blood pressure (BP) of less than 100 millimeters of mercury (mmHg)
• Diagnosed with orthostatic hypotension defined as a decrease in systolic blood pressure of equal to or greater than 20 mmHg or a decrease in diastolic blood pressure of equal to or greater than 10 mmHg when compared with BP from the supine position
• For US sites: have donated blood of more than 500 mL within the previous 3 months of screening or intend to donate blood during the course of the study
• For Singapore sites: Have donated blood of more than 450 mL or more in the past 3 months or provided any blood donation within the past 1 month before screening
• Consume more than 10 cigarettes per day (or the equivalent) or are unable or unwilling to abstain from nicotine
• Have alcohol intake that exceeds recommended alcohol consumption limits per local regulation or are unwilling to stop alcohol consumption 24 hours prior to dosing until discharge
• For Part D, has concurrent use or anticipated use of phosphodiesterase 5 inhibitor such as vardenafil, tadalafil, and sildenafil, soluble guanylyl cyclase activators (such as riociguat and vericiguat)
• For Parts D and G, has concurrent or anticipated use of long-acting nitrates or nitric oxide (NO) donors
• For Part D, has current use of more than 3 mechanism of actions for treatment of hypertension
• For Part G, has previous or current diagnosis of primary glomerulopathy, vasculitic renal disease, prior dialysis or unstable rapidly progressing renal disease, autosomal dominant or autosomal recessive polycystic kidney disease, lupus nephritis, or anti-neutrophil cytoplasm antibody-associated vasculitis