The DX and HX of the 6th gen Civic share the same part # flywheel, which is about 20 lbs.
The VX flywheel, I noticed, is about double the price of a regular flywheel (from Honda). If you search parts places like AutoZone or AdvanceAuto, they don't have a direct replacement for the VX. Instead they give you the same flywheel all the other Civics use.
I keep finding more disadvantages to lighter flywheels than I do advantages. Check out this thread (was searching for stock flywheel weight):
Flywheel weight? - D-series.org
It seems the 7lbs region is very extreme, and shouldn't be used for street cars. Most of these "racers" prefer around 10lbs. If the VX is around 16lbs, that should be nice balance between the stock 20lbs and the more performance oriented weight. Again, we can only assume at this point if the decreased weight was for fuel economy, or because the VX motor had less power than standard Civic motors.
And I don't buy the claim that lightened flywheels increase HP by that much. They might free up some power because the motor doesn't have to build up speed in a heavier flywheel, but once you are at a steady speed the effects are minimal. Going back to California98Civic's point, a mildly light flywheel (12-16 lbs) could actually benefit P&G driving without effecting driving.