Recently a client asked why she was weight lifting when her main goal was fat loss. She said "it seems like just the opposite of what I have always heard."
The issue at hand is that there wasn't much scientific study on this topic. We have known about the effects of aerobic exercise for decades. Only recently has science shed light on weight training's calorie and fat burning effects.
Weight lifting burns calories while you are working out, but also (if done properly) elevates your resting metabolism. This means that you are burning more calories at rest over the course of the entire day. Note: at rest you get half of your energy from fat and half from carbohydrates, plus your body can use fat to help your muscles recover from each workout. Over time these calories add up. Of course, you have to create a calorie deficit by eating less calories than you use to see a significant change in your body.