You got to look at the wing airfoil to understand this.
Modern commercial transports use laminar flow airfoils which
utilize a drag polar 'bucket'. Where you are in the bucket
depends directly on your AoA. As the planes burn fuel during
cruise, step climbs into thinner air are performed to maintain
that optimal lowest-drag AoA.
Since these airplanes are designed for efficient cruise at higher weights
and high altitudes, when they get light and low, the AoA is too
shallow to keep the wing inside the low Cd area and drag actually increases.
The lighter the plane, the shallower the AoA at a given altitude.
-> the higher the drag from the wing.
So, at the same speed, the light plane will have more drag than
the heavy one and needs to do a steeper descend to maintain airspeed.
XPM