I would expect some low single digit percentage
Interesting assumption.
Assume A320 dimensions
Nose to tail = 37.57m
Wing span = 34.1m
Wing area = 122.6 m↑2
Average chord = 122.6/34.1 = 3.6m
Fwd C of G limit = about 15% MAC
Aft C of G limit = about 45% MAC.
Diff = 30% chord width = 1.08m
Assume aft C of G is at approximately 55% of fuselage length and elevator C of Lift is at 95% of fuselage length. (Diff = 37.57*40/100 = 15 m)
Therefore when C of G is at fwd limit, extra down force on tail = Mass * 1.08/15 = 0.066 * Mass (6.7% of Mass of Aircraft).
I don't know what the down force is on the tail at the Aft C of G position, but if the load is an extra 6.7% of the aircraft mass at the fwd limit then I'd guess the load is about 3% of M at the aft limit giving a total of about 10% M at the fwd limit.