Here's a counterpoint:
Weight is important, but not as important as drivetrain efficiency, or as aerodynamic drag. The reason is, that as you note weight adds to the kinetic energy, so you can reclaim it by coasting, and/or by using regenerative braking if it is a EV. So, yes it takes more to accelerate, but you can get back some of the energy you put in; preferably by coasting.
Aerodynamic drag though, is a total loss. And rolling friction (like wheel alignment, bearing friction, dragging brakes, and tire rolling resistance, etc.) are also total loss; but they are also fairly easy to minimize.
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