Do you burn calories by weightlifting?

The importance of building muscle is this: If you are losing weight and not doing resistance training, then you lose muscle as well as fat. So you can lose weight and keep the same amount of fat. Muscle actually burns calories while at rest, so it is in your best interest to do resistance training AND cardio. Since you're asking about burning calories I ume you want to lose weight, and nutrition is the vast, vast majority of doing that.