The restricted-to-free rotator phase transition of fatty acid monolayers has been modeled using a potential which represents the amphiphiles as planar cross sections of fourfold symmetry. Using much larger system sizes than paper I [D. R. Swanson, R. J. Hardy, and C. J. Eckhardt, J. Chem. Phys. 99, 8194 (1993)], Monte Carlo simulations of the isobaric-isothermal ensemble of model systems with varied number of objects were undertaken to study the effect of system size on the characteristics and order of the phase transition. A peak in the specific heat vs temperature curve was observed near the transition. For each system size, the maxima of the peak showed a linear dependence on the area, which is characteristic of a first order transition. The latter is further confirmed from the observation of a small "van der Waals" loop by increasing the volume at a constant temperature. The result of this simulation matches the qualitative behavior of experimental observations of monolayers, which undergo a weakly first order transition. Additional similarity with experiment was found by the determination that the simulated superfluid phase has the short range translational order and quasilong range bond orientational order characteristic of a hexatic phase.