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.

There is a weight associated with the electrons needed to convey information, but it's negligible.

Beyond that though, we're not actually so interested in moving the electrons, but in toggling the electric field. Most of the electrons in the wire stay in the wire, and any that leave are balanced by another coming in on the other end. Electrons can move between the atoms, but if your cable is actually changing the number then something has gone wrong, since laptops don't typically ionize copper.

It's a pretty straightforward calculation, since amperage is the number of electrons per second, and the cables has a well documented signaling rate.
It works out to a bit weighing about 2x10^-22 grams for a USB cable.

Data is essentially just fancy electric current. Current doesn't really 'flow' so much as propogate a wave similar to a newtons cradle desk toy. A physicist might chime in on this, but no, I don't think data being transmitted actually weighs anything.

Unless you factor in the interaction between any induction effects and the earths magnetic field. But it's beyond negligible.

It's only 4 wires, only 2 of which carry data. A 6ft cable transferring at a max usb speed of 80gb/s moving at the slow end of signal propagation through copper of .5c would have less than a kilobyte on it at any time.

He'll get the nerds in the lab to cook something up.