The high penetration of renewable energy has led to the widespread emergence of weak grids, under which grid-following (GFL) inverters suffer from dynamic instability induced by phase-locked loops (PLL). Although reducing the bandwidth of the PLL can enhance system stability, it significantly degrades the ability of the inverter to reject power interaction disturbances. The inherent trade-off between the bandwidth of the PLL and its disturbance suppression capability are investigated. A cooperative strategy through a grid-forming (GFM) inverter to improve the robustness of GFL inverters without requiring hardware modifications is introduced. The simulation results validate that the proposed strategy effectively suppresses power interaction disturbances and enhances system stability under weak-grid scenarios.