Deterministic positioning single site-controlled high symmetric InGaAs quantum dots (QDs) in (111)B-oriented GaAs photonic crystal cavities with nanometer-scale accuracy provides an idea component for building integrated quantum photonic circuits. However, it has been a long-standing challenge of improving cavity Q-factors in such systems. Here, by optimizing the trade-off between the cavity loss and QD spectral quality, we demonstrate our site-controlled QD-nanocavity system operating in the intermediate coupling regime mediated by phonon scattering, with the dynamic coexistence of strong and weak coupling. The cavity-exciton detuning-dependent micro-photoluminescence spectrum reveals concurrence of a trend of exciton-polariton mode avoided crossing, as a signature of Rabi doublet of the strongly coupled system. Meanwhile, a trend of keeping constant or slight blue shift of coupled exciton-cavity mode(CM) energy across zero-detuning is ascribed to the formation of collective states mediated by phonon-assisted coupling, and their rare partial out-of-synchronization linewidth-narrowing is linked to their coexisting strong-weak coupling regime. We further reveal the pump power-dependent anti-bunching photon statistical dynamics of this coexisting strong-weak coupled system and the optical features of strongly confined exciton-polaritons, and dark-exciton-like states. These observations demonstrate the potential capabilities of site-controlled QD-cavity systems as deterministic quantum nodes for on-chip quantum information processing and provide guidelines for future device optimization for achieving the strong coupling regime.