Muscle does not weigh more than fat; it is more dense than fat, and that saying is not quite right. A pound is a pound is a pound. A pound of fat takes up more room than a pound of muscle. So, say you lost a pound of fat but gained a pound of muscle in your butt. You would weigh the same, but your butt would be smaller and your pants would fir looser.
That's why your weight can stay the same but you lose inches. That's also why you should not soley focus on the scale. Myself, I wouldn't care if I weighed 200 lbs if I could fit in a size 10 jeans!
Think of it this way: a pound of lead bb's weighs the same as a pound of feathers. However, you could probably hold the bb's in your hand. You sure can't hold a whole pound of feathers in your hand!