Introduction: Extreme meteorological disturbances can interrupt centralized power grids and force local microgrids to operate as islanded, safety-critical energy processes. Conventional rule-based dispatch and discrete-action learning methods often react too late to weather alerts, causing premature battery depletion and critical-load interruptions. Methods: This study proposes a resilience-oriented process-control framework based on Proximal Policy Optimization (PPO). The microgrid energy management problem is formulated as a continuous Markov Decision Process that integrates time, photovoltaic and wind generation, battery state of charge, critical and non-critical load demands, and a binary meteorological alert signal. A dynamic multi-objective reward function shifts the controller from cost-aware operation during normal conditions to defensive scheduling during disaster alerts, prioritizing critical-load continuity while limiting battery degradation and excessive load shedding. The framework is evaluated through a 72-hour typhoon-induced outage scenario using high-resolution meteorological profiles representative of northern Taiwan, with rule-based control and Deep Q-Network strategies as benchmarks. Results: The PPO controller learns a proactive pre-disaster charging policy and tactical non-critical load curtailment after islanding. Across five independent simulation runs, the proposed framework achieves a 98.5% critical-load survival rate, reduces cumulative critical-load outage to 0.72 hours, and lowers battery chattering to 18 cycles, outperforming rule-based control and DQN baselines. Conclusions: The results indicate that PPO-based continuous control can improve the resilience, stability, and operational safety of microgrid processes under extreme weather uncertainty. The proposed framework provides a practical machine-learning-based control strategy for climate-resilient energy systems and critical infrastructure protection.