"Muscle does not weight more than fat.
HOWEVER
Muscle is denser and weighs more BY VOLUME than fat."
That just means: Muscle does weigh more than fat. Agreed
Lets not confuse two issues: Water weighs more than air means Water is heavier than air. Gold weighs more than water means Gold is heavier than water.
Muscle weighs more than fat means muscle is heavier than fat.
Playing with words, you start getting: 'A pound of fat weighs the same as a pound of muscle' which is obviously true - but as Pete explains above, the simple fact is, Muscle is heavier than fat.
Therefore, if there were two people, Person A and person B. Person A has more muscle than B, then person A will appear thinner than person B, even though they are of the same weight. This is because Person A has more muscle.
I hope this clarifies things, as a lot of websites have the silly 'A pound of this is the same as a pound of that rubbish'.
Ask for some fat from your butcher next time, whip out the kitchen scales, and try it yourself