I seriously doubt that you would notice the difference in power required for cruise with different weights.
an aeroplane has two force couples at work.
thrust and drag
weight and lift
out on an arm at the back is the horizontal stabiliser.
lift can be taken as acting through the centre of pressure.
weight acts through the centre of gravity.
lift is pretty well locked in position by the geometry of the wing and moves forward and aft with angle of attack dependent on the characteristics of the aerofoil used.
weight will be affected by the position of the variable loads in the aeroplane.
it also can move during flight as fuel is burnt off.
the limits of where all this can sit and have the aircraft remain controllable were established during initial test flying of the aircraft, the results of which are simplified for the pilot in the weights and loads charts.
in flight if the two force couples balance out fully the horizontal stabiliser will sit out back needing to do nothing. all good and well but the trim will seem a little waffly.
if we move the cg slightly forward of the centre of pressure and use some downlift from the horizontal stabiliser we get a more stable trim.
there is more to it but you can figure it out from the texts.