The benefit of weight loss in patients with obesity and heart failure with reduced ejection fraction (HFrEF) is controversial. Semaglutide has shown cardiovascular (CV) risk-reduction and impact on CV risk factors including overweight, dysglycaemia and hypertension in subjects with type 2 diabetes (T2D). The STEP-HFpEF (Semaglutide Treatment Effect in People With Obesity and HFpEF) recently demonstrated, at 1-year, to not only reduce weight considerably, but also significantly improve health-related quality of life, functional status scores and 6-min walk distance in patients with heart failure with preserved ejection fraction (HFpEF). Also, the recently concluded SELECT trial was the first CV outcome trial with semaglutide in patients with overweight or obesity and established CV disease, including heart failure (but no T2D). Semaglutide demonstrated a 20% reduction in MACE, defined as the composite of cardiovascular death, non-fatal myocardial infarction, and non-fatal stroke. These landmark findings have important implications for clinicians -as they mean that weight loss and/or semaglutide as anti-obesity pharmacotherapy could be a treatment strategy for secondary prevention of CV disease in patients with overweight or obesity. It is, however, unknown whether weight loss with either calorie-restricted diet or semaglutide has beneficial effects in obese subjects with heart failure and reduced ejection fraction. Also it is unclear whether semaglutide has cardiovascular benefits irrespective of starting weight and amount of weight loss. Purpose: The study aims to investigate whether weight loss treatment with semaglutide is superior to weight loss with calorie-restricted diet in improving peak oxygen uptake in patients with obesity and heart failure with reduced ejection fraction.