In this study we will investigate how the medicine cagrilintide affects bone health in women after menopause with obesity during weight loss, compared to treatment with placebo (the dummy medicine with no active substances) and semaglutide. The purpose is to examine whether cagrilintide can reduce the decline in bone mass associated to weight loss. Participants will either get cagrilintide, semaglutide, CagriSema (cagrilintide combined with semaglutide), or placebo. Which treatment participants get is decided by chance. Semaglutide is already approved for the treatment of overweight and obesity and can be prescribed by doctors. Cagrilintide and CagriSema are new medications currently under development for weight management. The study will last for about 79 weeks.