This study will look at how much cagrilintide helps people with overweight or obesity lower their body weight. Cagrilintide is a new investigational medicine. Doctors may not yet prescribe cagrilintide. Participants will either get cagrilintide or placebo. Which treatment participants get is decided by chance. Participants are two times more likely to get cagrilintide than placebo. Like all medicines, the study medicine may have side effects. Possible side effects will be followed carefully during the study. For each participant, the study will last for about 1 year and 6 months.