We investigated the magnetic properties of the low-dimensional BaM2Si2O7 (M = Cu, Co, and Mn) system using both experimental measurements and theoretical calculations. Magnetization, specific heat, and single crystal neutron diffraction measurements have been performed on single crystal BaMn2Si2O7. The spin structure was determined and a magnetic phase diagram with applied field along the b axis was constructed, which contains a spin flop transition around 6 T. Magnetization and specific heat measurements confirmed the presence of weak ferromagnetism in BaCo2Si2O7. Furthermore, we performed local-spin density approximation with on-site Coulomb energy (LSDA+U) calculations for the BaM2Si2O7 (M = Cu, Co, and Mn) system. Based on the first-principles calculations, the origin of the magnetic differences of the three materials is discussed.