Both PDR1 and Mustafagander have it right. The system that I know best has a tubular capacitor mounted vertically and a flat-plate capacitor at the bottom of the tank where it is always covered by fuel. The flat-plate capacitor provides a reference point so that no matter what the temperature or the type of fuel is in the tank, the system has a point from which to calculate and display the weight of the fuel. Fill a plane with warm fuel in the daytime and the next morning the weight reading will remain the same even though the fuel temperature has dropped overnight.

I have to say I have strong doubts that the dielectric constant of fuel depends only on the density (and not also on the exact chemical makeup, dissolved water, etc.) It would make sense to have a flat plate capacitor on the bottom of the tank to determine the dielectric constant of the fuel, so that the fuel level can then accurately be calculated from the capacitance of the vertical probe. That would give you volume, but not mass.

The only fuel density meter I could find on Google measures the attenuation of a vibrating disc submerged in the fuel.