RecruitingPhase 4Drug trialDoes Semaglutide Improve Depressive Symptoms in Patients With Major Depressive Disorder and Overweight or ObesityThis 26-week long, double-blinded randomized clinical trial aims to investigate the effects of semaglutide once-weekly vs. placebo on depressive symptoms in 116 patients with Major Depressive Disorder (MDD) and co-existing overweight or obesity. The treatment will be an add-on treatment to the patient's usual medication. The investigators hypothesize that adjunctive treatment with semaglutide, will lead to a significant improvement in mood compared to placebo in patients with MDD and overweight or obesity. The primary endpoint is the change in depressive symptoms measured as difference in the 12-item self-report mood questionnaire Major Depression Inventory (MDI) from start to follow-up after 26 weeks. The MDI measures the extent to which symptoms of depression have been present in the past two weeks.