Small-angle neutron scattering (SANS) measurements are reported on a sterically stabilized, core-shell colloidal system using contrast variation. Aqueous dispersions of polystyrene particles bearing grafted poly(ethylene glycol) (PEG) have been studied over a large range of particle concentrations and two different solvent conditions for the PEG polymer. SANS data are analyzed quantitatively by modeling the particles as core-shell colloids. In a good solvent and under particle contrast conditions, an effective hard-sphere interaction captures excluded-volume interactions up to high concentrations. Contrast variation, through isotopic substitution of both the core and solvent, expedite a detailed study of the PEG layer, both in the dilute limit and as a function of the particle concentration. Upon diminishing the solvent quality, subtle changes in the PEG layer translate into attractions among particles of moderate magnitude.