CG location vs total weight

[Xavier Mouraux]

Hello all,

I am trying to clarify an idea about CG location for different weight of a same airplane. 

Goals: 
Minimize the effect of elevator trim /stab incidence on level flight, inverted flight and verticals.
The airplanes need to fly at the same speed independent of its weight or the qty of fuel.

Questions:
Could it be that a heavier plane need a CG more AFT than the same plane with a lower weight to "set" in the proper angle of attack ?
Could it be useful to locate the tank so the CG move FWD as the fuel is burned ?
What about CG recommendation on plan or from other pilots with same plane but different weight ?
How much change in angle of attack is required on a pattern plane for a 2lb difference in weight to fly at the same speed ?
What would be the effect on elevator sensitivity ?
Am I going too far ?

Any opinion ?

Xavier
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