This study is open to adults who are at least 18 years old and have a body mass index (BMI) of 27 kg/m2 or more. People can take part if they have cardiovascular or chronic kidney disease. People who have at least 2 health problems related to their weight or risks of cardiovascular disease can participate. Participants must have previously tried to lose weight by changing their diet.

The purpose of this study is to find out whether people with overweight or obesity who take a medicine called survodutide (BI 456906) are less or more likely to develop serious cardiovascular problems. It also aims to find out whether health parameters like blood pressure improve. Overweight and obesity are linked to cardiovascular disease. Survodutide is a medicine that is developed to help people with obesity or overweight to lose weight.

Participants are divided into 3 groups of almost equal size. 2 groups get different doses of survodutide and 1 group gets placebo. Placebo looks like survodutide but does not contain any medicine. Every participant has a 2 in 3 chance of getting survodutide. Participants inject survodutide or placebo under the skin once a week. All participants also receive counselling on diet and physical activity.

Participants are in the study for up to 2 years and 3 months. During this time, it is planned that participants visit the study site up to 21 times and attend remote visits by video calls. During these visits, the doctors check participants' cardiovascular and overall health. The results are compared between survodutide and placebo groups. The study staff also takes note of any unwanted effects.

Inclusion Criteria:

1. Male or female, age ≥18 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) ≥27 kg/m2 at screening with established cardiovascular disease (CVD) and/or at least 2 weight-related complications or risk factors for CVD OR BMI ≥30 kg/m2 at screening with established CVD or chronic kidney disease (CKD), and/or at least 2 weight-related complications or risk factors for CVD.

Further inclusion criteria apply.

Exclusion criteria:

1. Previous treatment with glucagon-like peptide-1 receptor (GLP-1R) agonists within 3 months before screening.
2. Type 1 diabetes.
3. Less than 3 months between the last dose of GLP-1R agonists and GLP-1R agonist/insulin/glucose-dependent insulinotropic polypeptide (GIP) combinations and screening.
4. Known clinically significant gastric emptying abnormality (e.g., severe diabetic gastroparesis or gastric outlet obstruction).

Further exclusion criteria apply.

Once the criteria in section 'time frame' are fulfilled, researchers can use the following link https:// www.mystudywindow.com/msw/datasharing to request access to the clinical study documents regarding this study, and upon a signed "Document Sharing Agreement". Furthermore, researchers can request access to the clinical study data, for this and other listed studies, after the submission of a research proposal and according to the terms outlined in the website.

After structured results have been posted, all regulatory activities are completed in the US and EU for the product and indication, and after the primary manuscript has been accepted for publication.

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.