Cyberspace weighs less than two ounces.. Russel Seitz took estimates for size and traffic of the entire Internet, and used this with the weight of the energy used to move a byte of information around. Although minuscule individually, over trillions and trillions of bytes it slowly added up. How large is the Internet? According to Russel Seitz: two ounces.
It gets complicated, in fact defining electricity gets extremely complicated, and I'm certainly no physicist.
Suffice it to say that electricity - either in the form of a charge or as electromagnetic energy (which is what most people think of when they use the word 'electricity') has no weight. It affects other things which do have weight, however, and I think that's probably what Russel Seitz is talking about.