But F = ma. Once the bike gets moving, you [no] longer need to keep your motor running in order to maintain speed
This is only true if you ignore gravity, aerodynamic drag, rolling resistance, mechanical friction, etc etc..
In reality: when you are travelling on a flat road, you are primarily slowed down by aerodynamic drag ("the wind"). When you are travelling up hill of a certain steepness, gravity becomes the primary source of resistance.
This page has a nice interactive calculator for such things..
Specifically, with the gradient set to 0%, the "force required to overcome gravity" (Fgravity) is of course zero. Weight makes little difference, except to rolling resistance, which is dwarfed by the force required to overcome aerodynamic drag (Fdrag)
Then, increase the gradient to, say, a reasonably steep 10%. Suddenly the Fgravity becomes the significant factor. Changes in weight make substantial difference to the power required for a given speed
For example, if I start with the default numbers on that page: to climb a 5% gradient at 20km/h would require 291watts. If I reduce the bike from 8kg to 6kg, the power becomes 285watts. For comparison, I have ridden an average of 291watts for 16mins, vs 285w for 16min30.