"Muscle does not weigh more than fat, any more than lead weighs more than feathers. A pound is a pound is a pound. Where the misunderstanding often comes in is that muscle is much more dense than fat, so that, by volume, it seems to weigh more. That is, a pound of muscle occupies less space than a pound of fat. In addition, because a pound of muscle burns more fat than a pound of fat, even at rest, by increasing your lean muscle tissue mass, you're helping your body burn more calories.
If you only have a small amount of weight to lose, then you may feel like the weight training is not helping you move down on the scale. In fact, the number may even go up, but you will look thinner. This is due to an increase in lean body mass (muscle, bone, blood volume) and a decrease in body fat. In other words, even if the scale doesn't change much, you will probably see a difference in how your clothes fit."