NaFeAs is a quasi-2D pnictide parent compound with a weak magnetic moment and separate structural and antiferromagnetic transitions.Because Co doping leads to a superconductor with Tc~ 20 K at a very low optimal doping of x =0.02, NaFe1-xCoxAs is uniquely suited to sensitive studies of the cohabitation and competition between magnetism and superconductivity.Using NMR as a local probe of both antiferromagnetic order and superconductivity, we have compared Knight shifts and relaxation rates on the Na, As, and Co nuclei.Above Tc, we find weak doping inhomogeneity, in the form of residual paramagnetic regions with differing TN values, and a strongly field-controlled magnetic volume.Below Tc, we observe a strong competition between antiferromagnetism and superconductivity, in which the temperature is the dominant control parameter, suppressing the magnetic volume fraction very significantly in favor of the superconducting one, while the external field suppresses Tc.Our results suggest both a microscale phase separation in real space and in reciprocal space a competition between two order parameters requiting the same electrons on the quasi-2D Fermi surface.