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We interpret and model the statistical weak lensing measurements around130,000 groups and clusters of galaxies in the Sloan Digital Sky Surveypresented by Sheldon et al. 2007 (Paper I). We present non-parametricinversions of the 2D shear profiles to the mean 3D cluster density and massprofiles in bins of both optical richness and cluster i-band luminosity. Wecorrect the inferred 3D profiles for systematic effects, including non-linearshear and the fact that cluster halos are not all precisely centered on theirbrightest galaxies. We also model the measured cluster shear profile as a sumof contributions from the brightest central galaxy, the cluster dark matterhalo, and neighboring halos. We infer the relations between mean cluster virialmass and optical richness and luminosity over two orders of magnitude incluster mass; the virial mass at fixed richness or luminosity is determinedwith a precision of 13% including both statistical and systematic errors. Wealso constrain the halo concentration parameter and halo bias as a function ofcluster mass; both are in good agreement with predictions of LCDM models. Themethods employed here will be applicable to deeper, wide-area optical surveysthat aim to constrain the nature of the dark energy, such as the Dark EnergySurvey, the Large Synoptic Survey Telescope and space-based surveys.

Cross-correlation Weak Lensing of SDSS galaxy Clusters II: Cluster Density Profiles and the Mass--Richness Relation