But how do you compensate for the weight of the chickenfeed (variable) and
the byproducts (Variable, and smelly)

Use a catapult, so that every time a bird steps to the center during the
sampling interval, he's catapulted into a wall. (taking care of the
territoriality problem)
Use a video camera to mark the impact point, and calculate the weight from
the trajectory. The expended chicken then slides into a bag labelled "Mc
Nuggets".