Polymer nanoparticle composites (PNCs) with ultrahigh loading of nanoparticles (NPs) (>50%) have been shown to exhibit markedly improved strength, stiffness, and toughness simultaneously compared to the neat systems of their components. Recent experimental studies on the effect of polymer fill fraction in these highly loaded PNCs reveal that even at low polymer fill fractions, hardness and modulus increase significantly. In this work, we aim to understand the origin of these performance enhancements by examining the dynamics of both polymer and NPs under tensile deformation. We perform molecular dynamics simulations of coarse-grained, glassy polymer in random-close-packed NP packings with a varying polymer fill fraction. We characterize the mechanical properties of the PNC systems, compare the NP rearrangement behavior, and study the polymer segmental and chain-level dynamics during deformation below the polymer glass transition. Our simulation results confirm the experimentally observed increase in modulus at low polymer fill fractions, and we provide evidence that the source of mechanical enhancement is the polymer bridging effect.