As well as the four forces lift, drag, thrust and weight there are also several torques acting on an aircraft that must be in balance to stop it pitching up/down. These act about the centre of gravity.
a) The Wing produces a nose down torque (A "pitching moment" not shown below).
b) The center of pressure isn't exactly on the CoG so that also produces a pitch down.
c) The tail produces a pitch up.
These must sum to zero or the aircraft rotates about the CoG. It's why a tail is needed in the first place.
Altering the CoG position effects b) so c) must be adjusted to compensate. As others have said the further aft the CoG the less downforce the tail must produce. The further forward the more down force the tail must produces and the more lift the wing must produce to keep overall lift and weight in balance. Increased lift = increased drag.
On a canard (tail first aircraft) the foreplane ADDS to the overall lift produced..
