The brushless doubly-fed induction generator (BDFIG) presents significant potential for application in wind power systems, primarily due to the elimination of slip rings and brushes. The application of virtual synchronous control (VSynC) has been demonstrated to effectively augment the inertia of BDFIG systems. However, the dynamic characteristics and stability of BDFIG under weak grid conditions remain largely unexplored. The critical stabilizing factors for BDFIG-based wind turbines (WTs) are methodically investigated, and an enhanced VSynC method based on linear active disturbance rejection control (LADRC) is proposed. The stability analysis reveals that the proposed method can virtually enhance the stability of the grid-connected system under weak grid conditions. The accuracy of the theoretical analysis and the effectiveness of the proposed method are affirmed through extensive simulations and detailed experiments.