The perovskite SrIrO3 is an exotic narrow-band metal owing to a confluence of the strengths of the spin-orbit coupling (SOC) and the electron-electron correlations. It has been proposed that topological and magnetic insulating phases can be achieved by tuning the SOC, Hubbard interactions, and/or lattice symmetry. Here, we report that the substitution of nonmagnetic, isovalent Sn4+ for Ir4+ in the SrIr1-xSnxO3 perovskites synthesized under high pressure leads to a metal-insulator transition to an antiferromagnetic (AF) phase at TN > 225 K. The continuous change of the cell volume as detected by x-ray diffraction and the lamda-shape transition of the specific heat on cooling through TN demonstrate that the metal-insulator transition is of second-order. Neutron powder diffraction results indicate that the Sn substitution enlarges an octahedral-site distortion that reduces the SOC relative to the spin-spin exchange interaction and results in the type-G AF spin ordering below TN. Measurement of high-temperature magnetic susceptibility shows the evolution of magnetic coupling in the paramagnetic phase typical of weak itinerant-electron magnetism in the Sn-substituted samples. A reduced structural symmetry in the magnetically ordered phase leads to an electron gap opening at the Brillouin zone boundary below TN in the same way as proposed by Slater.