You are correct when you say that weight will act as an horizontal component of lift when banked (Wsin(theta)). This component acts to oppose the turning moment created by the asymmetrical thrust, reducing the rudder pressure required, hence more controllability with the same fin.
You are also correct in your observation that the thrust line will also change with an increase in weight. The P-factor is moving a matter of inches, while the sin(theta) component of the weight easily offsets this change. A change of thrust of 1 foot (from let’s say 8.58 to 9.58) would change the moment by 11%. This change of thrust is rather large, being about ¼ the radius of a typical prop, but let’s suppose. Now a change of weight from 14,000 to 16,000 is a 14% increase. I really can’t imagine the p-factor moving out that far, but alas I have no hard data on the distance that P-factor moves. Guess I really didn’t positively answer your question. But I think the weight increase offsets the p-factor, after all how much is your AoA going to change, 2 or 3 degrees?