The data exists as electricity, and while electrons have mass, there's always going to be roughly the same number of electrons in the cable. They're flowing in a loop across the cable, so more electrons aren't needed for more data. It's the pattern they move in that carries the data (kinda).

At least that's my simplistic view of it. There's probably some technicalities I'm glossing over, but I think the point stands that a cable carrying more data isn't heavier due to that data.