As CG is aft, means it is closer to the point where the lift force is created. So the nose down moment is smaller (moment=force x distance). In an airliner design, the tail should always create a nose up moment about the CG to overcome the nose down moment created by lift. In another word, the total moment should be equal to zero, so result is a balanced flight (second part of Newton`s first law).
Now, as the nose down moment is smaller, the required nose up moment by tail needs to be smaller as well. So this requires less downward force created by tail.
For balanced flight, it should be
L=W+Ftail (First part of Newton`s first law).
As Ftail is smaller, L needs to be smaller as well. So if L is less, required AOA is less. If AOA is less drag is less. If Drag is less, fuel burn is less
L=Required Lift (upward)
W=Weight of the airplane (downward)
Ftail= Tail created force (downward)