On geological timescales the Earth's dipole moment can vary between 0.1 and 2 times the present value. The weakest internal magnetic fields occur during geomagnetic polarity transitions when the Earth's internal dipole field reverses. Theoretically, the size of the paleomagnetosphere is expected to change in the function of the dipole moment according to a power law scaling relation. We carried out a series of numerical magnetohydrodynamic (MHD) simulations of axial dipolar paleomagnetospheres, gradually decreasing the relative dipole moment from 1 to 0.1, in order to test the validity of the theoretical scaling relations for different values of the north-south interplanetary magnetic field component (IMF Bz). We study the dipole moment dependence of the standoff distance, the flank distances, and the polar cap size, and derive power law scaling relations with significantly differing scaling exponents as compared to the theoretically expected ones. The extent of deviation from the theoretical scaling exponents is controlled by the magnitude of the southward Bz. We quantify the Bz-dependence of the size of the magnetosphere and validate our results with the Roelof-Sibeck bivariate function of magnetopause shape obtained from in-situ satellite measurements for the present-day magnetosphere. We conclude that the Roelof-Sibeck function cannot be applied for southward Bz values stronger than 5 nT. A new Bz-dependent dipole scaling relation is suggested for the magnetospheric scale size. Inserting our corrected scaling relation in the Hill model of magnetosphere-ionosphere coupling, a better fit can be obtained between simulated and theoretically calculated paleomagnetospheric transpolar potentials.