Remember, that weight training is more effective than cardio for burning fat, since it burns calories after the session is over, unlike cardio which pretty much only burns calories during the session.
Something that is made for building muscle is essential during a cut to help prevent loss of lean mass. So don't feel like the heavy weights are a waste of time, since you won't be gaining any muscle. On the contrary, heavy weights are more important than light weights when on a cut. Muscle loss is a very serious issue while cutting. If you could only do one during a cut, either cardio or weight training, you would want to pick weight training.