Wearable and ambient sensors have been increasingly used for unique remote health monitoring applications. In this work, we propose an Internet of Medical Things (IoMT) architecture based on automated sensing of physiological and ambient parameters, to detect the risk of obesity in individuals. Timely assessment of obesity risk could improve the quality of life for patients in future as it would help to reduce the probability of chronic diseases such as diabetes. The architecture uses Body Mass Index (BMI) of patient as an input parameter which is a key measure to indicate obesity. Furthermore, we also propose to integrate the proposed IoMT architecture with the emerging scheme of Federated Learning (FL). FL has been used to recommend the appropriate fitness routine for the users. MATLAB simulations for the proposed FL algorithm has been performed and the variations in the loss functions have been observed.