This seems to be surprisingly complex !
As an example (using the Cessna Graph and some guessed weights)
IF 2000 lbs and 100 knots is 'typical', this will probably have an angle of attack of 5 and CD of 0.05
IF one adds 400 pounds (which is a lot in to an aircraft previously 2000 all up), you will need to increase the angle of attack to 6 at a constant airspeed) and increase the Cd to 0.06 (20%) which will result (if we keep the power constant) in a speed reduction of 6% (cube root of 1.2). It will be slightly less because we always cruise above our minimum drag speed, so the Cd will be somewhat reduced due to our slower speed reducing parasitic drag more than the increase in induced drag from the higher angle of attack needed at slower speed (vs the above calculated effect of the higher AoA needed for increased weight).
HOWEVER, In many planes the increase in weight will also result in the CG moving aft, which as previously discussed reduces the drag due to the reduced downward force on the tail. So for many aircraft, the difference between light+forward CG and heavy+aft CG could be negligible.