There is no objective way to prove whether or not it is hate. There is no way to prove beyond a shadow of a doubt that the action was hate related or if the person is just not very tactful.

A combination of exercise and diet because diet alone will only cause you to lose weight in muscle and other things like water. Exercise alone will only cause the fat cells in your body to shrink but once you eat again with your unhealthy habits, they expand again. This causes a yoyo effect which can make it harder to lose weight in the future. If you use a combination of both, you get the benefits of both without the consequences. Also, you would receive the added bonus of being an overall physically healthy person which can also improve mental and emotional health.