The less a motor vehicle weighs, the less work (energy) it takes to move it around.

Units of Work

Whenever a new quantity is introduced in physics, the standard metric units associated with that quantity are discussed. In the case of work (and also energy), the standard metric unit is the Joule (abbreviated "J"). One Joule is equivalent to one Newton of force causing a displacement of one meter. In other words,

The Joule is the unit of work.
1 Joule = 1 Newton * 1 meter
1 J = 1 N * m
1 J = 1 kg * m/s^2 * m

In fact, any unit of force times any unit of displacement is equivalent to a unit of work. Notice that the amount of force (Newtons) is dependent on mass (kilograms). The less a motor vehicle weighs, the less force it takes to move it, and the less energy is required.

This is a direct relationship. Reduce mass by any percentage and you will reduce energy consumption and the cost of energy by the same amount.