We present adaptive optics spectro-imaging observations of the RW Aur jet in optical forbidden lines, at an angular resolution of 0.4''. Comparison with HST data taken 2 years later shows that proper motions in the blueshifted and redshifted lobes are in the same ratio as their radial velocities, a direct proof that the velocity asymmetry in this jet is real and not an emissivity effect. The inferred jet inclination to the line of sight is i = 46+/- 3 degr. The inner knot spacing appears best explained by time variability with at least two modes: one irregular and asymmetric (possibly random) on timescales of le 3-10 yr, and another more regular with =~ 20 yr period. We also report indirect evidence for correlated velocity and excitation gradients in the redshifted lobe, possibly related to the blue/red velocity and brightness asymmetry in this system. Based on observations collected at the Canada-France-Hawaii Telescope (CFHT), operated by the National Research Council of Canada, the Centre National de la Recherche Scientifique, and University of Hawaii.