Well I'm not sure I understand the question, but here's my take.
The hydrostatic equation is this: dP/dz = - density*gravity
That is, the change in pressure with height is a function of the gravitational (almost) constant and the density of the air. In other words a cold airmass (dense) is thin, and a warm airmass (not dense) is thick.
Most weather models use the hydrostatic assumption, otherwise the equations go crazy (trying to solve nonlinear equations with a linear calculator poses many problems). The hydrostatic assumption isn't valid, however, in thunderstorms because of the large pressure and density perturbations caused by vigourous updrafts.