I think heavy means it's still loaded with fuel.
Heavy means it's a Jumbo Jet.
Heavy is a category of a/c - there are 4 Light-Med-Lg and Heavy. If you are a heavy a/c, it has to do with talking with the tower, and weight turbulence and space betw. your a/c and others.
Heavy is a designation for a certain classification of aircraft, determined by its gross weight, like a 747, 777, etc.
Or a Cessna 172 with four people in it. :-)