This study will look at how well CagriSema helps people living with obesity to lose weight and maintain the weight loss long-term. The study has 2 parts: The first part is called 'the main study' and the second part is called 'the extension study'. In the main study participants will either get CagriSema (a study medicine) or placebo (a dummy medicine that looks like CagriSema but has no active ingredient). Which treatment participants get is decided by chance. Participants are two times more likely to get CagriSema than placebo. If participants get CagriSema in the main study, participants will continue on CagriSema in the extension study. Which dose of CagriSema participants will continue on is decided by chance. If participants get placebo in the main study, participants will get CagriSema in the extension study. Participants will take one injection of study medicine once a week. The study will last for about 3 years and 3 months.