COPD is a common disease characterized by pulmonary inflammation, reduced pulmonary capacity, reduced physical activity and quality of life. Obesity is likewise a common disease characterized by inflammation, reduced physical activity and quality of life. Targeting both obesity and inflammation may turn out beneficial for patients with COPD and obesity, and this study explore the possibility to reverse a vicious cycle of COPD, lack of physical activity and obesity. The primary objective of the study is to evaluate the effect of Liraglutide 3mg in patients with COPD on patient reported outcomes as measured by the Transition Dyspnea Index. The hypothesis is that Liraglutide 3mg exerts beneficial effects on measures of pulmonary function and quality of life in overweight patients with COPD by reducing body weight and reducing inflammatory activity.