to make this comparison, we assume that the two cars are identical (i.e., body, running gear, tires, etc) except in weight.

assuming both cars are accelerated with the same throttle opening, the heavier car will take longer to accelerate to the desired speed than the lighter car. At any point in time, the lighter car will have covered more distance than the heavier one - hence it will have more miles for a given gallon of fuel.

if you accelerate both cars at the same rate (assuming this is possible), the heavier car will require a wider throttle opening than the lighter one, and will use up more fuel for the given distance.

if you measure the fuel economy of both cars once they have reached the desired speed, their fuel consumption per distance should be the same.

however, this will not be EXACTLY the same, because the heavier car will have more internal friction than the lighter one, due to higher loads on the wheel bearings. Although this will tend to increase the fuel consumption (i.e. wider throttle opening to maintain the speed), this difference is almost negligible.

however again, all other things being equal, the heavier car will sit lower than the lighter one, and will have a smaller frontal area than the lighter one due to less tire frontal area. The drag coefficient would also probably be better in the lowered car, due to less turbulence created by the air flowing under the car. A smaller frontal area and drag coefficient will tend to lower fuel consumption for the heavier car in this case (i.e. smaller throttle opening to maintain the speed)