Muscle weighs the same as fat, that's true, in the sense of 1 pound of muscle = 1 pound of fat. A lb is a lb.
However, what most people mean by "muscle weighs more than fat" is that muscle is DENSER than fat. Meaning, 1 lb of muscle takes up less space than 1 lb of fat. Meaning, gaining 5 lbs of lean muscle tissue will take up less space than 5 lbs of fat tissue.
Here's a picture example:
See how that muscle takes up a LOT less space?
Now, yuo might be built like me. In the past two years, I have been the same height (5'7) and weighed anywhere between 120 and 145. I was actually skinnier at my heaviest, due to weight lifting and working out. At 145, I was almost down to a size 3. At 120, I was pushing a size 9.
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