How much does a fighter jet weigh?

Short answer: it depends on which one you're talking about.

The F-5 (a light fighter) weighs about 4,500 kg empty (7,000 kg loaded) while the F-15 is 12,700 kg empty (and 20,000 loaded).
Most fighter aircraft weigh around 11-12 metric tons when empty or about 16-20t when fully loaded.