Evaluation of the Tolerability of Cagrilintide in Participants Not Tolerating GLP-1-RA Therapies Due to Gastrointestinal Adverse Events

The purpose of this clinical study is to look at the safety of the medicine Cagrilintide when compared to placebo in people who do not tolerate marketed glucagon-like peptide-1 (GLP-1) therapies and who live with overweight or obesity. Participants will get either Cagrilintide (the treatment being tested) or Placebo (a treatment that has no active medicine in it). Which treatment participant will get is decided by chance. The study will last for about 8 months.

Key Inclusion Criteria: * Male or female (sex at birth) * Age 18 years or above at the time of signing the informed consent * History of documented treatment with GLP-1-RA medications with gastrointestinal (GI) adverse effects as the main reason for treatment discontinuation * Not suitable for re-initiation of GLP-1-RA treatment based on medical history and investigator judgement * Body mass index (BMI) greater than or equal to (≥) 30.0 kilograms per square meter (kg/m\^2) Key Exclusion Criteria: * Female who is pregnant, breast-feeding, or intends to become pregnant or is of childbearing potential and not using highly effective contraceptive methods * Treatment with GLP-1 receptor agonist or GLP-1-RA medication for any indication within 8 weeks before screening * History of type 1 or type 2 diabetes * Glycated haemoglobin (HbA1c) ≥ 6.5 percent (%) (48 millimole per mole \[mmol/mol\]) as measured by the central laboratory at screening * Treatment with glucose-lowering agent(s) prescribed for the indication of diabetes or pre-diabetes within 90 days before screening * Treatment with any medication prescribed for the indication of weight management within 8 weeks before screening