Did I find correct messages?
You are correct saying that there are a lot different weights. We are modelling the aircraft that has empty weight (pilot, oil, unusable fuel, wingtip launchers) 19900 lbs approximately. Plus 293 lbs for full drum of rounds. This amounts to 20200 lbs in total, which is very close to what you can see in the editor.
These numbers are for US F-16C bl.50. AFAIK, HAF F-16C bl.50/52 are even heavier as you've mentioned.
Also, don't forget that GE129 engine is heavier than the others.