Rare genetic forms of obesity, so called monogenic obesity are linked to alteration in energy balance involving hypothalamic pathways. More than 60 genes encoding for proteins located in the hypothalamic leptin/melanocortin pathway have been described in the French National Protocol for Diagnostic and Care (PNDS). The natural history of monogenic obesity is characterized by an early onset in childhood, with a major increase in weight in adolescence and young adulthood. The worsening of obesity exposes these patients to severe complications. Severe obesity and eating disorders have a major impact on the quality of life of the person but also of the family and caregivers. Clinical management is complex and requires comprehensive, specialized and multidisciplinary management. But the usual lifestyle approaches have so far shown disappointing results, similarly to bariatric surgery which leads to a more frequent weight regain in the situation of monogenic obesity, justifying new approaches. In this context, evaluating the response to treatment in the particular condition of monogenic obesity is crucial to propose therapeutic options as early as possible to limit weight evolution and its complications. GLP-1 (glucagon-like peptide 1) based innovative therapies have recently emerged as a promising option for treatment of obesity and its complications. This is the case for Semaglutide 2.4mg/week (WEGOVY®), developed by Novo Nordisk. However, there is a lack of data to confirm that semaglutide could be also effective in monogenic obesity. The hypothesis in this study is that treatment with Semaglutide 2.4mg/week (WEGOVY®) could be as effective in monogenic obesities as in common obesity.