This can get pretty long... but here's an attempt at a condensed version.
With the exception of some fighters airplanes are always designed so that the entire CG range is forward of the center of lift, thus making the airplane "nose-heavy" , the horizontal stabilizer is always producing some amount of down force to counteract this. This is done to make the aircraft stable in pitch.... If the the aircraft is disturbed, for instance, nose up... the resultant airspeed decrease would render the horizontal stab less effective and allow the nose to drop. And the opposite nose down. OK, so how does loading affect performance?
Because the CG is not co-located with the Center of Lift, any loads being created by the horizontal stabilizer must be carried by the wing in addition to the weight of the aircraft itself. For instance if a light airplane weighs 2000 lbs and its tail is producing 100 lbs of downforce to hold the nose up then the wing must lift 2100 lbs. The location of the center of gravity will effect the amount of downforce that the hor. stab. must produce, and thus the amount of lift the wing must produce. If an a/c is loaded to the aft limit it is a little less nose heavy and the hor. stab. doesn't need to produce as much downforce... if our 2000 lb. light airplane is loaded aft and our hor. stab. is only producing 50 lbs. of downforce then the wing need only lift 2050 lbs.
So in a nutshell... a C.G. further aft means the wing will fly at a lower angle of attack for any given airspeed and will produce less induced drag.... fuel savings.
Hope that helps!