A Study to Test How Well Different and Multiple Doses of BI 3034701 Are Tolerated in People Living With Overweight or Obesity

The main objectives of this trial are to investigate safety, tolerability of alternative dose titration strategies and pharmacokinetics (PK) of BI 3034701 in participants with overweight / obesity and at least one weight related co-morbidity following subcutaneous administration.

Inclusion criteria : 1. Male or female trial participant, overweight/obese with one weight related complication but otherwise healthy according to the assessment of the investigator, as based on a complete medical history including a physical examination, vital signs (blood pressure (BP), pulse rate (PR)), 12-lead electrocardiogram (ECG), and clinical laboratory tests 2. Age of 18 to 74 years (inclusive) 3. Body mass index (BMI) of 27.0 to 39.9 kg/m² (inclusive) 4. Signed and dated written informed consent in accordance with international council for harmonisation - good clinical practice (ICH-GCP) and local legislation prior to admission to the trial 5. Further inclusion criteria apply. Exclusion criteria: 1. Any finding in the medical examination (including blood pressure (BP), pulse rate (PR) or electrocardiogram (ECG)) deviating from normal and assessed as clinically relevant by the investigator, unless confirming the weight related complication 2. Repeated measurement of systolic blood pressure outside the range of 90 to 140 mmHg, diastolic blood pressure outside the range of 50 to 90 mmHg, or pulse rate outside the range of 50 to 90 bpm, unless arterial hypertension is the weight related complication in the context of this trial 3. Any laboratory value outside the reference range that the investigator considers to be of clinical relevance and may interfere with trial participation or interpretation of the results, other than abnormalities attributable to the permitted weight-related complications 4. Impaired renal function, defined as estimated glomerular filtration rate (eGFR) \