We present radial mass profiles within 0.3 r_vir for 16 relaxed galaxy groups-poor clusters (kT range 1-3 keV) selected for optimal mass constraints from the Chandra and XMM data archives. After accounting for the mass of hot gas, the resulting mass profiles are described well by a two-component model consisting of dark matter (DM), represented by an NFW model, and stars from the central galaxy. The stellar component is required only for 8 systems, for which reasonable stellar mass-to-light ratios (M/L_K) are obtained, assuming a Kroupa IMF. Modifying the NFW dark matter halo by adiabatic contraction does not improve the fit and yields systematically lower M/L_K. In contrast to previous results for massive clusters, we find that the NFW concentration parameter (c_vir) for groups decreases with increasing M_vir and is inconsistent with no variation at the 3 sigma level. The normalization and slope of the c_vir-M_vir relation are consistent with the standard LambdaCDM cosmological model with sigma_8 = 0.9. The small intrinsic scatter measured about the c_vir-M_vir relation implies the groups represent preferentially relaxed, early forming systems. The mean gas fraction (f =0.05 +/- 0.01) of the groups measured within an overdensity Delta=2500 is lower than for hot, massive clusters, but the fractional scatter (sigma_f/f=0.2) for groups is larger, implying a greater impact of feedback processes on groups, as expected.