What does "muscle weighs more than fat" actually mean?
Taken literally the phrase is nonsense — a kilogram of muscle and a kilogram of fat weigh exactly one kilogram each. What people mean is that muscle is denser than fat, so a given mass of muscle takes up less space.
The numbers: muscle tissue has a density of roughly 1.06 g/cm³, fat roughly 0.9 g/cm³. Muscle is therefore around 15–18% denser. That is a real difference but a smaller one than the phrase implies — muscle is not dramatically heavier by volume.
Why it matters is body composition. Two people at the same height and weight can look substantially different depending on how much of that weight is muscle versus fat. Someone who replaces three kilograms of fat with three kilograms of muscle weighs the same and is visibly smaller, because the muscle occupies less volume.
Where the phrase gets misused: it is often offered as reassurance to someone whose weight has not moved after weeks of training. Sometimes that is genuinely what is happening — particularly for beginners, who can gain muscle and lose fat simultaneously. But muscle is built slowly. A realistic rate for a trained person is a few hundred grams per month, and even a well-fed beginner is unlikely to exceed about a kilogram per month. If the scale has not moved in three months, muscle gain is unlikely to be the full explanation.
It also explains why BMI misclassifies muscular people. BMI uses only height and weight and cannot distinguish tissue types, so a heavily trained athlete can register as overweight while carrying very little fat.
Tape measurements, photographs and how clothes fit track composition change far better than weight alone.