Okay, let's try this way.
The stall warner works by sensing the stagnation point of the oncoming airflow -- where the oncoming air gets brought to a stop by the front of the wing. As the angle of attack increases, this stagnation point moves down and back along the bottom surface -- the flow either side of it (above and below) being away from the stagnation point. When the stagnation point passes over the little metal flap/small hole that makes up the stall warner, the local airflow changes (usually reverses direction) and the stall warner goes off.
Now, the angle of attack is directly proportional to the Coefficient of Lift (generally, within the attached region -- i.e.: pre-stall), which in turn is directly proportional to the Lift the wing's generating. Therefore, using a small amount of maths (and assuming no component of the aircraft's thrust acting in the vertical direction: true for small climb angles which will probably hold for a knackered PA28):
LIFT = WEIGHT
therefore WEIGHT = some constant x (angle of attack) x (Velocity)^2
where some constant ~ rho.(wing area)
therefore: for a lower weight and the same speed, the angle of attack required for steady, unaccelerated* flight is lower, therefore 1 up the stall warner should go off at a lower airspeed than fully loaded...
*and by unaccelerated, I'm including gz-loadings higher than 1...
And yes, stick position would make a nice indicator of alpha and I might be bothered and do the maths tomorrow morning...