You have one car that's 1,000 lbs and one that's 10,000 lbs. When you start each car, it will take a lot more energy to bring the 10k lb car up to the same speed as the 1k lb car, but after that, the effects of drag will weigh more heavily on the lighter car (F=ma, so the rate of deacceleration is a lot higher for a smaller mass), causing constant fluctuations in the motor shutting on and off.
With the the 10k car, the transitions would take much longer. The time in between accelerations would be longer, and the motor would be on for longer spurts. You gain a great deal of efficiency for simply leaving a mechanical system running vs constantly modulating a mechanical system (i.e. shutting it on and off).
This would work in favor of the heavy car being more efficient.
Of course, the heavier your car is the worse your 0-60 split would be, so for a performance car that's a negative.
Also, the heavier car would experience greater bearing resistance + friction. This is really difficult to quantify, and my gut is that it's outweighed by the momentum advantage.
But overall, for a car that ways 2k lbs, a 5% increase in mass is pretty negligible, especially for casual highway and local driving.