Under weak grid conditions, grid impedance is coupled with a control system for voltage source converter based high-voltage direct current (VSC-HVDC) systems, resulting in decreased synchronization stability. Unfortunately, most studies are based on the assumption that impedance ratio (R/X) is sufficiently small to ignore the effects of grid impedance. In this study, we establish a dynamic coupling model that includes grid impedance and control loops, revealing the influence mechanism of R/X on synchronization stability from a physical perspective. We also quantify the stability range of R/X in the static analysis model and introduce a sensitivity factor to measure its effect on voltage stability. Additionally, we utilize a dynamic analysis model to evaluate power angle convergence, proposing a corresponding stability criterion. We then present a method of synchronous voltage reconstruction aimed at enhancing the grid strength. Theoretical analysis shows that this method can effectively mitigate the effects of coupling between grid impedance and the controller under weak grid conditions, ensuring stable operation even under extremely weak grid conditions. Experiments validate the accuracy and effectiveness of the analysis and method.