Weight Loss in People Living With Overweight or Obesity Following Treatment With Cagrilintide

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.

Inclusion criteria: * Informed consent obtained before any study-related activities. Study-related activities are any procedures that are carried out as part of the study, including activities to determine suitability for the study * Female or male (sex at birth) * Age 18 years or above at the time of signing the informed consent * History of at least one self-reported unsuccessful dietary effort to lose body weight (a\*) * Body mass index (BMI) greater than or equal to \>= 30.0 kilogram per square meter (kg/m\^2), or 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 (a\*) Exclusion criteria: * History of type 1 or type 2 diabetes (a\*) * Treatment, or intention to initiate treatment, with any medication prescribed for the indication of weight management within 180 days before screening (a\*) * Previous dosing of marketed or non-marketed amylin-based compounds (a\*) (a\*) - As declared by the participant, reported in the medical records or at the investigator's discretion.