Weight reduction will have a minor affect on range. Unless you drive less than 30MPH and do virtually all of your driving in stop and go conditions. Since an EV drivetrain is so much more efficient than an ICE, the losses of accelerating the mass of the car is MUCH less. In other words, weight is much more important to an ICE, than it is for an EV.
At 30MPG the aerodynamic drag becomes the majority of the load on the drivetrain. And at 55MPH, aero drag is over 75%. Aero drag is a TOTAL LOSS.
The moving mass of the car can be (partially) used - by coasting most importantly. This is the whole point of driving, so once you have the car moving, the kinetic energy can be used to keep it moving. And when you need to slow down, we can use regen, to regain some of the energy invested in the moving car; with the additional losses of the motor to battery chain.