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.