How is V_S0 calculated for anything less than maximum weight? Is there a way to (safely) calculate the stall speed of an aircraft ($V_{S0}$) for anything below maximum weight? All the tables in the POH are valid for maximum weight only, and stall speed can drop significantly with a light load. As a consequence, if you're flying the published (max weight) $V_{ref}$ on final, you'll actually be carrying a significant amount of extra speed and thus increase the required landing distance, possibly in quite a dramatic fashion.
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: $$v_{reduced\,mass} = v_{full\,mass}\cdot\sqrt{\frac{reduced\,mass}{original\,mass}}$$