Yes, it does weigh something.
However, electrons weigh about 10^-31 Kg each.
That way, a you'll need about 10^31 electrons to make up a kilogram of them.
Bearing in mind that 10^6 is a million and 10^9 is a billion, 10^31 is an awful lot!
Taking the rough analysis further, let's look at your 1000 Watt microwave. This means that at full power, 1000 Joules of energy. Using the mains supply of 240V, this is about 4.2 Amps of current. In one second this is 4.2 Coulombs. Since a single electron has a charge of 1.6E-19 Coulombs, we have about 4.2E19 electrons per second. Given we know the mass of an electron, we can calculate that:
The mass of electricity in one second of microwave use is about 10^-12 Kg. That's a millionth of a milligram!
This is all very rough since I'm not including losses or power for the controls of the microwave, etc., but you get the point.
In summary, it does weigh something, but it's almost nothing.