A Research Study on How Well Cagrilintide and CagriSema Work in Children and Adolescents With Excess Body Weight

Inclusion criteria: * Informed consent of parent(s) or legally acceptable representative (LAR) of participant and child assent, as age-appropriate, 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. * The parent(s) or LAR of the child must sign and date the Informed Consent Form (according to local requirements) * The child must sign and date the Child Assent Form or provide oral assent (according to local requirements). * Male or female. * Aged 8 to less than (\<) 18 years at the time of signing the informed consent. * Body mass index (BMI), at screening, corresponding to: * Greater than or equal to (\>=) 95th percentile for children aged 8 to \< 12 years (Tanner stage 1-5) * \>= 95th percentile or \>= 85th percentile with the presence of at least one obesity-related complication including, but not limited to, type 2 diabetes (T2D), hypertension, dyslipidaemia or obstructive sleep apnoea for adolescents aged 12 to \< 18 years (Tanner stage 2-5). * Laboratory parameters, as measured by the central lab at screening, within normal sex- and age-specific ranges of total calcium, phosphate, alkaline phosphatase, parathyroid hormone. * History of at least one unsuccessful effort to lose sufficient body weight after participation in a structured lifestyle modification programme (diet and exercise counselling) for at least 3 months. * Body weight greater than (\>) 45 kilograms (kg) at screening. For participants with T2D at screening the following inclusion criteria also apply * Glycated haemoglobin (HbA1c) less than or equal to (\<=)10.0 percent (%) (86 millimoles per mole \[mmol/mol\]) as measured by central laboratory at screening. * Treatment with lifestyle intervention or treatment with metformin according to local label. * Treatment with metformin should be stable (same dose and dosing frequency) for at least 56 days before screening. Key exclusion criteria: * Treatment with any medication prescribed for obesity or weight management within 90 days before screening. * Previous or planned (during the study period) obesity treatment with surgery or a weight loss device. However, the following are allowed: * Liposuction and/or abdominoplasty, if performed \> 1 year before screening. * Adjustable gastric banding, if the band has been removed \> 1 year before screening. * Intragastric balloon, if the balloon has been removed \> 1 year before screening. * Duodenal-jejunal bypass liner (e.g., Endobarrier), if the sleeve has been removed \>1 year before screening. * Uncontrolled thyroid disease. * Endocrine, hypothalamic, or syndromic obesity. * A self-reported (or by parent(s)/LAR, where applicable) change in body weight \> 5 % within 90 days before screening irrespective of medical records. * Type 1 diabetes or monogenic diabetes. For participants without T2D at screening the following exclusion criteria also apply * HbA1c greater than or equal to 6.5% (48 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. For participants with T2D at screening the following exclusion criteria also apply * Known hypoglycaemic unawareness as indicated by the investigator according to Clarke's questionnaire. * Recurrent severe hypoglycaemic episodes within 1 year before screening, as judged by the investigator. * Positive insulinoma associated protein-2 (IA-2) antibodies or anti-glutamic acid decarboxylase (anti-GAD) antibodies. * Treatment with any medication for the indication of diabetes other than those stated in the inclusion criteria within 90 days before screening. * Uncontrolled and potentially unstable diabetic retinopathy or maculopathy. Verified by a fundus examination performed within 90 days before screening or in the period between screening and randomisation. Pharmacological pupil-dilation is a requirement unless using a digital fundus photography camera specified for non-dilated examination.