Small-angle neutron scattering (SANS) studies have been carried out to examine the evolution of interaction and structure in a nanoparticle (silica)-polymer (polyethylene glycol) system. The nanoparticle-polymer solution interestingly shows a reentrant phase behavior where the one-phase charged stabilized nanoparticles go through a two-phase system (nanoparticle aggregation) and back to one-phase as a function of polymer concentration. Such phase behavior arises because of the nonadsorption of polymer on nanoparticles and is governed by the interplay of polymer-induced attractive depletion with repulsive nanoparticle-nanoparticle electrostatic and polymer-polymer interactions in different polymer concentration regimes. At low polymer concentrations, the electrostatic repulsion dominates over the depletion attraction. However, the increase in polymer concentration enhances the depletion attraction to give rise to the nanoparticle aggregation in the two-phase system. Further, the polymer-polymer repulsion at high polymer concentrations is believed to be responsible for the reentrance to one-phase behavior. The SANS data in polymer contrast-matched conditions have been modeled by a two-Yukawa potential accounting for both repulsive and attractive parts of total interaction potential between nanoparticles. Both of these interactions (repulsive and attractive) are found to be long range. The magnitude and the range of the depletion interaction increase with the polymer concentration leading to nanoparticle clustering. At higher polymer concentrations, the increased polymer-polymer repulsion reduces the depletion interaction leading to reentrant phase behavior. The nanoparticle clusters in the two-phase system are characterized by the surface fractal with simple cubic packing of nanoparticles within the clusters. The effect of varying ionic strength and polymer size in tuning the interaction has also been examined.