The term electricity includes several different phenomena, but none of these have any weight. To weigh something (that is, to experience the Earth’s gravitational pull), an object needs mass. An electric current is created when charged particles move – eg electrons in a copper wire. While these electrons have a tiny amount of mass, they exist in the wire whether or not a current is applied, so the wire’s mass doesn’t change. The electric force (which causes particles with the same charge to repel each other, for instance) has no weight as forces don’t have mass. The only electric phenomenon which might arguably weigh something is the buildup of a static charge, when an object gains excess electrons. In this case, the extra electrons would add to the object’s mass, but the weight difference would be nominal.
Answered by Alex Cheung.