A Research Study to See How Well CagriSema Helps People With Excess Body Weight Lose Weight

This study has 2 parts: First part is the main study and second part is the extension study. During the main study participants will receive 1 of 4 study medicines. If participants continue in the extension study, they will not receive any study medicine during the extension. The main study will look at how well CagriSema helps participants with excess body weight lose weight compared to a "dummy" medicine and 2 other medicines, cagrilintide and semaglutide. Participants will either get CagriSema, cagrilintide,semaglutide or "dummy" medicine. Which treatment participants get is decided by chance. They will take one injection once a week. The study medicine is injected briefly with a thin needle, typically in the stomach, thighs or upper arms. Extension study: After the main study, not all participants will continue in the extension study. The study staff will tell the participant if they will continue or not into the extension study. In the extension study we will look at what happens to the participant's body weight and diseases related to excess body weight after the participant stops taking the study medicine. The main study will last for about 1½ years and the extension study will last for another 2 years.

Inclusion Criteria: * Male or female * Age above or equal to 18 years at the time of signing informed consent * Body mass index (BMI) greater than or equal to 30.0 kilograms per square meter (kg/m\^2) or b) BMI greater than or equal to 27.0 kg/m\^2 with the presence of at least one weight-related comorbidity including, but not limited to hypertension, dyslipidaemia, obstructive sleep apnoea or cardiovascular disease Exclusion Criteria: \- Glycaemia related: a) Glycated Haemoglobin (HbA1c) greater than or equal to 6.5 percent (48 millimoles per mole \[mmol/mol\]) as measured by the central laboratory at screening b) History of type 1 or type 2 diabetes mellitus