  (Abridged) We use Subaru data to conduct a detailed weak-lensing study of the
dark matter distribution in a sample of 30 X-ray luminous galaxy clusters at
0.15<z<0.3. A weak-lensing signal is detected at high statistical significance
in each cluster, the total detection S/N ranging from 5 to 13. In this paper we
concentrate on fitting spherical models to the tangential distortion profiles
of the clusters. When the models are fitted to the clusters individually, we
are unable to discriminate statistically between SIS and NFW models. However
when the tangential distortion profiles of the individual clusters are
combined, and models fitted to the stacked profile, the SIS model is rejected
at 6- and 11-sigma, respectively, for low- and high-mass bins. We also use the
individual cluster NFW model fits to investigate the relationship between
cluster mass (M_vir) and concentration (c_vir), finding an anti-correlation of
c_vir and M_vir. The best-fit c_vir-M_vir relation is: c_vir(M_vir) propto
M_vir^{-alpha} with alpha=0.41+/-0.19 -- i.e. a non-zero slope is detected at
2sigma significance. We then investigate the optimal radius within which to
measure cluster mass, finding that the typical fractional errors are improved
to sigma(M_Delta)/M_Delta ~ 0.1-0.2 for cluster masses at higher over-densities
Delta=500-2000, from 0.2-0.3 for the virial over-density (~110). Further
comparisons between mass measurements based on spherical model fitting and the
model-independent aperture mass method reveal that the 2D aperture mass
enclosed within a cylinder of a given aperture radius is systematically greater
than the 3D spherical mass obtained from NFW model fitting: M_2D/M_3D= 1.34 and
1.40 for Delta=500 and 110, respectively. The amplitude of this effect agrees
well with that predicted by integrating the NFW model along the line-of-sight.
