We report an experimental investigation of the two-dimensional J_{eff}=1/2 antiferromagnetic Mott insulator by varying the interlayer exchange coupling in [(SrIrO_{3})_{1}, (SrTiO_{3})_{m}] (m=1, 2 and 3) superlattices. Although all samples exhibited an insulating ground state with long-range magnetic order, temperature-dependent resistivity measurements showed a stronger insulating behavior in the m=2 and m=3 samples than the m=1 sample which displayed a clear kink at the magnetic transition. This difference indicates that the blocking effect of the excessive SrTiO_{3} layer enhances the effective electron-electron correlation and strengthens the Mott phase. The significant reduction of the Néel temperature from 150 K for m=1 to 40 K for m=2 demonstrates that the long-range order stability in the former is boosted by a substantial interlayer exchange coupling. Resonant x-ray magnetic scattering revealed that the interlayer exchange coupling has a switchable sign, depending on the SrTiO_{3} layer number m, for maintaining canting-induced weak ferromagnetism. The nearly unaltered transition temperature between the m=2 and the m=3 demonstrated that we have realized a two-dimensional antiferromagnet at finite temperatures with diminishing interlayer exchange coupling.