Muscle does NOT weigh more than fat, any more than rocks weigh more than feathers. A pound is a pound is a pound. Where the confusion 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. This is why taking your body measurements is so crucial! You may find yourself frustrated as you work out and see an increase in 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 and your body measurements!