Simply put:
The heavier aircraft would overspeed if it tried to descend at the same angle as the lighter one!
Because it has more power at its disposal, all the way down, by surrendering potential energy
Along the same lines of Capt Pit Bull's
Rate of Descent = Power Deficit / Weight.
This also requires the assumption that the drag of an aircraft does not go up in proportion to it weight - and of course it doesn't.