Interfacing a weak grid imposes challenges on distributed generators (DGs). These challenges include transient frequency and voltage dynamics that can destabilize the system. Accordingly, this paper investigates the grid stiffness based on different scenarios and the dynamics of a grid feeding DG connected to a weak grid. Moreover, the dynamic effects of the physical and control parameters on the system’s stability are deeply analyzed and evaluated. Specifically, complete mathematical models and graphical representation are carried out to precisely examine the impact of the system parameters on the stability and performance of the DG. Therefore, stable deployment of renewable energy resources into power networks can be achieved as well as an efficient and robust performance of DGs can be ensured when connected to weak grids. The obtained results show the importance of the performed study in optimal sizing and designing the output filter of the inverter and the impact of tuning the control parameters on the system dynamics. As a result, a proper design of system physical and control parameters can be accurately achieved considering all factors affect the system performance. The paper also conducts detailed and elaborated analyses and simulations to evaluate the performance of a PI-controlled RC damped inverter connected to a weak grid. The proposed filter design of the interfacing inverter can significantly extend the integration of DGs into microgrids without requiring complex control schemes or oversized components.