Weight Loss in People Living With Overweight or Obesity and Type 2 Diabetes Following Treatment With Cagrilintide

This study will look at how much cagrilintide helps people with overweight or obesity and type 2 diabetes lower their body weight. Cagrilintide is a new investigational medicine. Doctors may not yet prescribe cagrilintide. Participant will either get cagrilintide or placebo. Which treatment participant 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. For each participant, the study will last for about 1 year and 6 months.

Key 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) \>= 27.0 kilogram per square meter (kg/m\^2).(a\*) * Diagnosed with type 2 diabetes \>= 180 days before screening. * Treatment with either lifestyle intervention(a\*), or: * Stable treatment (same drug(s), dose and dosing frequency) for at least 90 days before screening with 1-3 marketed oral antidiabetic drugs (metformin, α-glucosidase inhibitors (AGI), glinides, sodium-glucose cotransporter 2 inhibitor (SGLT2i), thiazolidinediones, Dipeptidyl peptidase-4 inhibitor (DPP-4i) or sulphonylureas (SU) as a single agent or in combination according to local practice.(a\*) * For up to 30% of participants the following concomitant medication is allowed: * Treatment for any indication with a stable dose of glucagon-like peptide-1 (GLP-1) containing medication, stable for at least 1 year before screening (a\*) and/or * Treatment with basal insulin minimum (0.25 units per kilogram per day (U/kg/day) or 20 units per day \[U/day\]) stable for at least 90 days before screening.(a\*) Key Exclusion Criteria: * Treatment, or intention to initiate treatment, with any medication prescribed for the indication of weight management within 180 days before screening.(a\*) * Treatment with glucagon-like peptide-1 (GLP-1) receptor agonist (RA) or GLP-1 containing medication within 180 days before screening, apart from those randomized according to inclusion criteria 7bi.(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.