Hydrostatic pressure effects on the temperature- and magnetic field dependencies of the in-plane and out-of-plane magnetization of the bi-layered perovskite Sr3Ru2O7 have been studied by SQUID magnetometer measurements under a hydrostatic helium-gas pressure. The anomalously enhanced low-temperature value of the paramagnetic susceptibility has been found to systematically decrease with increasing pressure. The effect is accompanied by an increase of the temperature Tmax of a pronounced peak of susceptibility. Thus, magnetization measurements under hydrostatic pressure reveal that the lattice contraction in the structure of Sr3Ru2O7 promotes antiferromagnetism and not ferromagnetism, contrary to the previous beliefs. The effects can be explained by the enhancement of the inter-bi-layer antiferromagnetic spin coupling, driven by the shortening of the superexchange path, and suppression, due to the band-broadening effect, of competing itinerant ferromagnetic correlations.