We measured NMR and magnetic susceptibility for the quasi-two-dimensional, weakly XY-like, spin-1/2 square-lattice Heisenberg antiferromagnet [CuCl(pyz)(2)]BF4 (pyz = pyrazine = N2C4H4) near the critical temperature. The Neel temperature T-N and the order-parameter critical exponent beta were obtained from the NMR line broadening as a function of temperature. As the applied field strength (H parallel to c) was increased, T-N increased and beta decreased. This behavior indicates that the field effectively enhanced XY anisotropy. The susceptibility as a function of temperature did not show a clear feature for T-N, but showed field-dependent minima below T-N for both H parallel to c and H parallel to ab, where minimum features disappeared for mu H-0 > 2T.