More often then not, when people say this, its because they are not comprehending what exactly they are saying.
What weights more…
A pound of feathers?
Or a pound of rocks?
The answer… They weight the same. One pound.
However what people are meaning to say is muscle is more dense, and if muscle was to fill the whole space of a certain weight fat, it’d weight more.
Here is an image of 2.2 kilos or about 5 pounds of fat on the left and muscle on the rig
What you will notice is that they weight the exact same, yet muscle is about 2/3 the size.
Important pieces to take from this:
A pound is a pound no matter what item it is.
Muscle is smaller per pound than fat.
If your weight isn’t moving but inches are being lost and clothing is fitting better, you are losing fat and building muscle tone.
The scale is not the only measure of results.
A few other ways to track progress and improvements/changes is:
Performance (strength metric and volume/time metric)
Body fat percentage
Clothing fit gage
Energy levels/sleep quality