ORIGINAL: madmodelman
Harry, surely in normal level flight at X mph aerodynamic forces would take any inbalace loads out of the equation. It's only when its static and low speeds that there is any load on the servo.
The ideal location of the pivot is at the aerodynamic centre. That way, the stab generates no aerodynamic load even at full deflection. It has no tendency to be blown back to neutral by the airflow and therefore no aerodynamic force to help cancel the imbalanced weight. On the full size light plane I fly with all moving tail this causes a problem in that the elevator would have no feel, the stick could be moved to any location and it would stay there, it would have no neutral, it would not get progressively harder to pull more and more elevator, so the tail has an anti-servo tab on its trailing edge that deflects like an elevator to generate a progressive force in order to give some feel and a neutralising tendency. In a model we have powered controls with no direct link from stick to surface, the feel and the neutralising comes from the springs in the tx. Thus the ideal all moving stab is pivoted at its AC and mass balanced, that way it presents barely any load to the servo at any position, except for when you move the control the servo has to accelerate the mass.
If you put the pivot point behind the AC then the stab becomes unstable and will try to flip backwards, generating huge forces on the servo. If the pivot is ahead of the AC the stab will be stable and yes the airflow will try to centre it thus helping to counter any weight imbalance, but the aerodynamic force will increase with the amount of travel and with airspeed and requires a stronger and stronger servo and linkages to overcome it.
H
PS the above applies to a stab which has a symmetrical section. If it is non symmetrical then it will generate a rotating force around the AC. For example, the F-4 Phantom and Tornado are inverted sections which will generate a leading edge upwards rotation, the amount of torque being dependent upon airspeed so even if mass balanced they will create a force for the servo even at neutral which gets strogner as you go faster.