You burn more fat and increase metabolism only if you have no food in your stomach and what you ate the night before has already been digested. However, if you are weight training, you are not going to have enough fuel to supply the energy to perform the set appropriately to create a stimulation that can cause growth and an increase in metabolism that you are ultimately looking for.
What matters most is the amount of calories you put in during the day verses what you expended, and putting back the eight pounds of muscle tissue that burns four hundred calories per day back on your body. (That is if you are a 35-40 year old man- worse if you are older)
Pick the time of day that you are going to have no excuses to not workout, and workout to fatigue on your first workout! Also, understand what you need to eat in a day to burn more fat. That’s how you will get leaner quicker; not just lose weight.