If you're painfully curious and want to know the textbook answer, most of the aircraft we fly are certified originally to an FAA Part 23 basis, for which the definition of the design speeds can be found here:
14 CFR 23.335.
The long and short of it is that at V_A, you should be able to apply full deflection
in any singular control axis and not damage the aircraft. The weight dependancy simply comes from rearranging F=ma to a = F/m; As you decrease the aircraft's mass, you will have a greater accelaration. Since you want a constant accel (say, 6G), you reduce the speed such that you stall first.
Key thing to note is that V_A says nothing about cyclic application of controls - If you swing the rudder from stop to stop with abandon, even below V_A, don't be surprised if the tail falls off!
