Muscle doesn't actually weigh more than fat. They both weigh the same. 1 lb. of muscle weighs the same as 1 lb. of fat. Obviously
The thing is, you can fit more muscle in the same space as you can fat - because it's more dense. You can fit 10 lbs of muscle in the same space as you could have normally fit 3 lbs of fat (that may not be exact but you get the idea). A guy that's the exact same size as his twin, but is full of muscle, will weigh more, because he has more muscle in him than his twin brother. You can cram more muscle in the same space than fat.