How is V_S0 calculated for anything less than maximum weight?
All aerodynamic forces are proportional to the dynamic pressure, which is the product of air density $\rho$ and half of the square of flight speed $\frac{1}{2}v^2$. If your flight mass is reduced, reduce the dynamic pressure proportionally to keep all other parameters the same. To express this in terms of speed, you need to multiply the posted speed in the handbook with the square root of the mass ratio, like that: $$v_{reduced\,mass} = v_{full\,mass}\cdot\sqrt{\frac{reduced\,mass}{original\,mass}}$$