Inclusion Criteria:
* Age 18 to 75 years (inclusive) at time of informed consent.
* BMI ≥30 and ≤50 kg/m², OR BMI ≥27 and \<30 kg/m² with at least 1 weight-related comorbidity (hypertension; dyslipidemia; or cardiovascular disease such as ischemic CVD or NYHA Class I-II heart failure).
* Motivated and able/willing to self-inject (or have trained assistance if needed) and follow study procedures, including lifestyle advice and questionnaires.
* Subgroup (NAFLD addendum): liver fat content ≥10% by MRI-PDFF (for participants invited to the addendum).
* Male and/or female; contraception requirements apply; women of childbearing potential must have negative pregnancy tests at specified visits and should not be breastfeeding.
* Capable of giving signed informed consent and complying with protocol requirements.
Exclusion Criteria:
* History of diabetes mellitus (type 1 or type 2), ketoacidosis, or hyperosmolar state/coma.
* Screening lab values suggestive of diabetes (HbA1c ≥6.5%; fasting glucose ≥126 mg/dL; or random glucose ≥200 mg/dL).
* Self-reported change in body weight \>5 kg within 3 months prior to screening.
* Prior or planned surgical treatment for obesity (exceptions: liposuction/abdominoplasty \>1 year prior).
* Current/planned endoscopic or device-based obesity therapy, or device removal within last 6 months (e.g., intragastric balloon, gastric artery embolization).
* Renal impairment: eGFR \<45 mL/min/1.73 m² (CKD-EPI) at screening.
* Clinically significant gastric emptying abnormality (e.g., severe gastroparesis) or chronic drugs affecting GI motility.
* History of acute or chronic pancreatitis (exception for resolved gallstone pancreatitis post-cholecystectomy).
* TSH outside 0.4 to 6.0 mIU/L at screening (with protocol-defined exceptions).
* Obesity due to other endocrine disorders (e.g., Cushing's) or monogenic/syndromic obesity (e.g., Prader-Willi).
* Psychiatric exclusion criteria including unstable major depressive disorder/severe psychiatric disorder within 2 years; lifetime suicide attempt; PHQ-9 score ≥15; or specified Columbia-Suicide Severity Rating Scale (C-SSRS) findings within past month.
* Uncontrolled hypertension (systolic ≥160 mmHg and/or diastolic ≥100 mmHg) or elevated resting pulse rate (\>100 bpm) at baseline.
* Recent (within 3 months) major cardiovascular events (e.g., MI, stroke, unstable angina, CHF hospitalization); tachyarrhythmia syndromes; NYHA Class III-IV CHF; or ECG abnormalities interfering with interpretation.
* Acute/chronic hepatitis or liver disease other than NAFLD; or screening labs: ALT \>3× ULN, ALP \>1.5× ULN, or total bilirubin \>1.5× ULN (with exception).
* Elevated calcitonin at Visit 1 per protocol thresholds; personal/family history of medullary thyroid carcinoma or MEN2.
* Active/untreated malignancy or remission \<5 years (with protocol exceptions for certain in-situ/skin cancers).
* Contraindication to GLP-1 receptor agonists, or other conditions that could prevent protocol compliance (including drug/alcohol abuse or eating disorder), per investigator judgment.
* Alcohol consumption \>14 units/week (women) or \>21 units/week (men).
* Recent marijuana/THC-containing product use within 3 months or unwillingness to abstain during trial (protocol exception for cannabidiol oil if agrees to refrain).
* Organ transplant history (except corneal transplant) or awaiting transplant.
* Hematologic conditions interfering with HbA1c measurement; recent large blood donation/transfusion/severe blood loss; hemoglobin below protocol thresholds.
* Severe atopy/multiple severe allergies or severe hypersensitivity reactions.
* Fasting triglycerides \>500 mg/dL at screening (with stability requirement for lipid-lowering therapy).
* Significant active, uncontrolled medical condition or history posing risk or interfering with data interpretation, per investigator judgment.
* History of symptomatic gallbladder disease within past 2 years (protocol-defined exceptions after cholecystectomy).
* History of documented HIV infection.
* Chronic systemic glucocorticoid therapy within 3 months or active autoimmune abnormality likely to require systemic steroids during study (with specified formulation exceptions).
* Recent medications that may cause significant weight gain (e.g., tricyclic antidepressants, atypical antipsychotics, mood stabilizers) within 3 months.
* Recent use (within 3 months) of medications or remedies intended to promote weight loss (examples listed in protocol, including GLP-1 RAs).
* Use of metformin or other glucose-lowering medications (e.g., for PCOS or diabetes prevention) not permitted at entry.
* Started implantable/injectable contraceptives within 18 months prior to screening (IUDs allowed if used ≥3 months).
* Known allergies to GLP-1 receptor agonists or LY3437943.
* Currently enrolled in another investigational study or recent participation/treatment within 30 days (or 5 half-lives, whichever longer).
* Previously received LY3437943 in this or another study.
* Investigator site personnel directly affiliated with the study and/or their immediate family; or Lilly employees.
* Note: The publicly posted protocol references additional exclusion criteria numbered 52-57 in a separate protocol addendum (not included in the posted protocol PDF).
