This study is open to adults between 18 and 74 years of age and who have a body mass index (BMI) of 30 kg/m2 or more, or a BMI of 27 kg/m2 or more and at least 1 health problem related to their weight. People who have previously not managed to lose weight by changing their diet can participate. People with type 2 diabetes cannot take part in this study.

The purpose of this study is to find out whether a medicine called BI 3034701 helps people living with obesity or overweight to lose weight. This study has 7 groups of participants. Groups 1 to 6 get different doses of BI 3034701; Group 7 gets placebo. Placebo looks like BI 3034701 but does not contain any medicine. Every participant has more than an 80% chance of getting BI 3034701. Participants receive 2 injections of BI 3034701 or placebo under their skin for 42 weeks. In addition to the study medicine, all participants receive counselling to make changes to their diet and to exercise regularly.

Participants are in the study for about 10 months. During this time, they visit the study site 15 times. The study doctors regularly measure the participants' body weight and take necessary laboratory tests. Participants also answer questions about their well-being and note their food intake and physical activity in diaries. The results will be compared between groups of participants to see whether the treatment works. The study doctors also regularly check participants' health and take note of any unwanted effects.

Inclusion criteria:

1. Male or female, age ≥18 to <75 years at the time of signing informed consent, and at least the legal age of consent in countries where it is >18 years
2. Body mass index (BMI) ≥30 kg/m² at screening, OR BMI ≥27 kg/m² at screening with the presence of at least 1 weight-related complication.
3. History of at least one self-reported unsuccessful dietary effort to lose body weight
4. Signed and dated written informed consent in accordance with International Conference on Harmonisation-Good Clinical Practice (ICH-GCP) and local legislation prior to admission to the trial. Persons must be capable of giving informed consent independently
5. Women of childbearing potential (WOCBP) must be ready and able to use highly effective methods of birth control per International Conference on Harmonisation (ICH) M3 (R2) that result in a low failure rate of less than 1% per year when used consistently and correctly. A list of contraception methods meeting these criteria and instructions on the duration of their use will be provided in the participant information sheet and in protocol.
6. In the investigator's opinion, participants are well-motivated, capable, and willing to: Sign the informed consent form (ICF); Learn how to self-inject the investigational medicinal product (IMP)(s) in the abdomen as required for this protocol (persons with physical limitations who are not able to perform the injections must have the assistance of an individual trained to inject the IMP(s)) OR Inject the IMP or accept injection from a designated person; Follow study procedures for the duration of the study, including, but not limited to: follow lifestyle advice (for example, dietary restrictions and physical activity plan), maintain diaries, complete required questionnaires, and handle the IMP(s) as described in the instructions for use (IFU)

Exclusion criteria:

1. Body weight increase or decrease (self-reported) of greater than 5% in the 3 months prior to screening
2. Treatment with anti-obesity medication and/or body weight change-inducing medication within 3 months before screening
3. Prior surgery of the gastrointestinal (GI) tract that could interfere with body weight including minimally invasive/endoscopic bariatric devices and any bariatric or metabolic surgery involving resection, sleeve gastrectomy, or bypass procedures (e.g. Roux-en-Y, one-anastomosis gastric bypass, duodenal-jejunal bypass sleeve), regardless of whether the device or bypass was removed. The following are allowed: (1) liposuction and/or abdominoplasty, if performed >1 year before screening, (2) lap banding, if the band has been removed >1 year before screening, (3) intragastric balloon, if the balloon has been removed >1 year before screening
4. 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, leptin deficiency, or Prader Willi Syndrome)
5. A Haemoglobin A1c (HbA1c) ≥6.5% (≥48 mmol/mol) as measured by the central laboratory at screening
6. History of type 1 diabetes mellitus (T1DM) or type 2 diabetes mellitus (T2DM) or treatment with glucose-lowering agent starting within 3 months before screening
7. Use of glucagon-like-peptide-1 receptor (GLP-1R), glucose-dependent insulinotropic polypeptide receptor (GIPR), glucagon receptor (GCGR) or neuropeptide Y receptor 2 (NPY2R) agonists (or the combinations thereof) within 3 months before screening
8. Answered "yes" to any of the suicide-related behaviours (actual attempt, interrupted attempt, aborted attempt, preparatory act or behaviour) or to the non-suicidal self-injurious behaviour question on the "Suicidal Behaviour" section of the Columbia-Suicide Severity Rating Scale (C-SSRS) related to the past 2 years before screening visit up to and including the randomisation visit Further exclusion criteria apply.

Clinical studies sponsored by Boehringer Ingelheim, phases I to IV, interventional and non-interventional, are in scope for sharing of the raw clinical study data and clinical study documents. Exceptions might apply, e.g. studies in products where Boehringer Ingelheim is not the license holder; studies regarding pharmaceutical formulations and associated analytical methods, and studies pertinent to pharmacokinetics using human biomaterials; studies conducted in a single center or targeting rare diseases (in case of low number of patients and therefore limitations with anonymization). For more details refer to: https://www.clinicalstudies.boehringer-ingelheim.com/msw/datasharing

One year after the approval has been granted by major Regulatory Authorities and after the primary manuscript has been accepted for publication, or after termination of the development program.

For study documents -upon signing of a 'Document Sharing Agreement'. For study data -1. after the submission and approval of the research proposal (checks will be performed by the sponsor and/or the independent review panel, including checking that the planned analysis does not compete with sponsor's publication plan); 2. and upon signing of a legal agreement.