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Kinetic energy, which you've termed "theoretical weight energy", and is every bit as theoretical as gravity, is conservative. That is to say, when you add kinetic energy to a car, that energy is not consumed or dissipated, but 100% of it is stored in the car. The same is true of work done against gravity: it is stored as gravitational potential energy, and 100% of it will be released when you bring the car back to the velocity or elevation where you started.
The fact that kinetic and gravitational energy are conservative mean that their impact on fuel economy is ZERO, provided that you never have to brake.
You can calculate kinetic energy to estimate the fuel consumption impact of braking. When you brake to a stop, you lose 1/2*m*Vē, where V is your initial velocity and m is your mass. As cr45 mentioned, weight has no place in a discussion of kinetic energy.
Weight does play a part in rolling resistance, though...
If you'd like a wiki article on how to do some math to estimate fuel consumption, I'd be happy to tap out something on the road load equation. Aero and rolling resistance are far more important to fuel economy than anything else, and should be given a proper treatment in the wiki.
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