Okay, 3 legs:
w1 x1 + w2 x2 + w3 x3 = 0 ; moment in x-axis
w1 y1 + w2 y2 + w3 y3 = 0 ; moment in y-axis
w1 + w2 + w3 = W ; force balance.
These 3 equ can be solved for three unknowns, ie the w's.
Now throw in a fourth leg, a w4, you have a problem because there is no fourth eqn.