A Study of Eloralintide (LY3841136) and Eloralintide With Tirzepatide in Participants With Overweight or Obesity

Inclusion Criteria: * Have safety laboratory test results within normal reference range for the population or investigative site, or results with acceptable deviations that are judged to be not clinically significant by the investigator. Participants with a history of thyroid disease or on thyroid medication will need to be biochemically euthyroid as assessed by measuring thyroid stimulating hormone at screening * Have a body mass index (BMI) within the range of 27.0 to 40.0 kilogram per square meter (kg/m²), inclusive * Have had a stable weight for the 3 months prior to screening, that is, less than 5% body weight change Exclusion Criteria: * Have known allergies to related compounds of eloralintide or tirzepatide, or any of the components of the formulations * Have significant previous or current history of comorbidities 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 been diagnosed with Type 1 or Type 2 diabetes mellitus, or have glycated hemoglobin greater than or equal to 6.5% or 48 millimole per mole (mmol/mol) * Have a history of any malignancy within the past 5 years except for basal cell or squamous epithelial carcinomas of the skin that have been resected with no evidence of metastatic disease for 3 years * Have a history or presence of a gastrointestinal (GI) disorder or previous surgery that impacts gastric emptying for example, gastric bypass surgery or pyloric stenosis * Have obesity induced by other endocrinologic disorders for example, Cushing syndrome, or diagnosed monogenetic or syndromic forms of obesity for example, Melanocortin 4 Receptor deficiency or Prader Willi syndrome * Have a history of hypocalcemia or hypercalcemia, or abnormal laboratory values for calcium or serum phosphorus * Have a medical history or current evidence of clinically significant cardiac condition, as per the investigator, including: * second or third degree heart block * sick sinus syndrome * peripheral arterial circulatory disorders * valvular disease * cardiomyopathy, or * other clinically significant cardiac condition * Have taken approved or investigational medication for weight loss, including GLP-1 RAs, within the previous 3 months of study screening * Intend to use any weight loss medications during study participation