A battery energy storage system (BESS) employing virtual synchronous generator (VSG) control is an effective means to enhance frequency stability in islanded microgrids. Improving traditional VSG control with model predictive control (MPC) can significantly strengthen its ability to suppress grid frequency fluctuations. However, conventional MPC-VSG schemes do not consider the impact of real-time state-of-charge (SOC) variations on the frequency regulation capability of the BESS. To address this issue, this paper proposes a dynamic weight-adaptive MPC-VSG frequency control strategy. First, a prediction model of the VSG is established according to its state-space equations. To balance BESS operational safety with bidirectional support for system frequency, the SOC and system frequency deviation are introduced to adaptively adjust the weight coefficients of the MPC cost function. Second, the adaptive rules partition the SOC into intervals based on the actual charging and discharging capabilities of the BESS, and S-shaped functions are employed to construct smooth transition bands between adjacent intervals, thereby enhancing control continuity and stability. Finally, simulation results show that the proposed method not only improves the dynamic frequency characteristics of isolated microgrids but also effectively mitigates battery overcharging or over-discharging issues.