Weak-grid operation, with a low short-circuit ratio (SCR), degrades voltage and frequency regulation and impacts the power control performance of inverter-based resources, triggering oscillations. This paper proposes a community-scale battery energy storage system (BESS)-supported grid-forming control scheme, where the grid-forming inverter acts a virtual synchronous generator (VSG). A grid-connected BESS-powered VSG model with cascaded voltage-current dual-loop control is developed to assess the impacts of line impedance and P-Q coupling on weak-grid connection and stability. In addition to the conventional VSG, dq-axis decoupling, virtual impedance, and adaptive inertia-damping (J-D) are incorporated and evaluated through multi-scenario MATLAB/Simulink simulations. The results indicate that virtual impedance effectively suppresses coupled oscillations, and the coordinated J-D adaptation yields the most pronounced peak mitigation during edge disturbances (e.g., fault clearance and load shedding). In particular, under a 50% three-phase voltage sag, the coordinated strategy reduces the post-clearance peaks of vpcc,rms and ipcc,rms by approximately 79.9% and 93.5%, respectively, and decreases the intensity of frequency fluctuations by approximately 97.6%. Overall, the proposed community-scale BESS-VSG scheme enhances the dynamic stability of voltage and frequency under weak-grid conditions and provides a practical control framework for engineeringoriented weak-grid support studies.