Most stall warning systems rely on direct or indirect sensing of angle of attack, not speed. So they 'know' the weight of the aircraft because they are using AoA, and a heavier aircraft at the same speed will have a higher AoA.
Similarly, most systems will therefore 'know' what 'g' you are at. An aircraft at 1.4Vs at 1'g' flight will have no warnings under normal conditions. Put that same aircraft in a 2'g' turn (or try to - it's going to stall at 1.96 'g' (1.4*1.4)) amnd there should be a bunch of noises or whatever trying to attract your attention.