People say that muscle weighs more than fat. That's like the old kids riddle: "Which ways more, a pound of feathers or a pound of bricks?" They both weigh the same. A pound of one item weighs exactly the same as a pound of something else. What's really different is the volume. A pound of fat takes up 503 ml so if you have excess weight in the form of fat, just 4 pounds takes up the volume of a two liter bottle of soda. That's a lot to lug around.
A pound of muscle only take up about 427 ml. This isn't a big difference if you're comparing it to the volume of fat, but does explain how two people who weigh the same can look different. Muscle is tight and compact, but fat is loose, squishy and jiggly.
Comparing muscle volume to fat volume is something that really only holds value for the skinny-fat segment of society. That was me. I have a pair of jeans that are labeled size 3/4. They look good on me, but I mainly bought them because of the poor sizing. I am probably a size 6/8, but I can fit into these jeans. The last time I fit into them comfortably, I weighed at least 8 pounds less than I currently do. I was not fit, though. I was merely thin. I have removed some of those soda bottles of fat and added muscle, so I take up less space.
I look back at pictures from January of 2010 and know that I weigh about the same as I did at that point, yet I am firmer and tighter than I was then. I can fit into smaller clothes than I did at that point. That is the present that weight lifting and real fitness have given me. It's the same present that you can give to yourself.