Most people don't realize that too much carbohydrate intake can inhibit the metabolization of fats for energy. This is caused by the excess production of insulin to metabolize the sugars. Excess insulin also inhibits the production of the growth hormone and the metabolization of fats for energy. So, fat-free or not, it may still get stored as fat. Without getting too much into nutrition here, just be advised that excess sugars are not the answer to weight loss.
Weight training requires energy to perform the actions.
What you don't burn, gets stored. So, fat burning occurs all day long even after the weight training session is over. Remember, muscle doesn't build in the gym, it builds when you rest and mostly when you sleep during the muscle repair cycle. This type of exercise is anaerobic, meaning that oxygen is not utilized during the energy production cycle, therefore, fat is not burned since oxygen is required for fat burning. Circuit Training is somewhat aerobic.