We have systematically changed the number of atomic layers stacked in 2D SnO nanosheet anodes and studied their sodium ion battery (SIB) performance. The results indicate that as the number of atomic SnO layers in a sheet decreases, both the capacity and cycling stability of the Na ion battery improve. The thinnest SnO nanosheet anodes (two to six SnO monolayers) exhibited the best performance. Specifically, an initial discharge and charge capacity of 1072 and 848 mAh g-1 were observed, respectively, at 0.1 A g-1. In addition, an impressive reversible capacity of 665 mAh g-1 after 100 cycles at 0.1 A g-1 and 452 mAh g-1 after 1000 cycles at a high current density of 1.0 A g-1 was observed, with excellent rate performance. As the average number of atomic layers in the anode sheets increased, the battery performance degraded significantly. For example, for the anode sheets with 10-20 atomic layers, only a reversible capacity of 389 mAh g-1 could be obtained after 100 cycles at 0.1 A g-1. Density functional theory calculations coupled with experimental results were used to elucidate the sodiation mechanism of the SnO nanosheets. This systematic study of monolayer-dependent physical and electrochemical properties of 2D anodes shows a promising pathway to engineering and mitigating volume changes in 2D anode materials for sodium ion batteries. It also demonstrates that ultrathin SnO nanosheets are promising SIB anode materials with high specific capacity, stable cyclability, and excellent rate performance.