The magnetic structure and electronic ground state of the layered perovskite Ba2IrO4 have been investigated using x-ray resonant magnetic scattering. Our results are compared with those for Sr2IrO4, for which we provide supplementary data on its magnetic structure. We find that the dominant, long-range antiferromagnetic order is remarkably similar in the two compounds and that the electronic ground state in Ba2IrO4, deduced from an investigation of the x-ray resonant magnetic scattering L3/L2 intensity ratio, is consistent with a Jeff=1/2 description. The robustness of these two key electronic properties to the considerable structural differences between the Ba and Sr analogues is discussed in terms of the enhanced role of the spin-orbit interaction in 5d transition metal oxides.