Regional disaster resilience quantifies the changing nature of physical risks to inform policy instruments ranging from local immediate recovery to international sustainable development. While many existing state-of-practice methods have greatly advanced the dynamic mapping of exposure and hazard, our understanding of large-scale physical vulnerability has remained static, costly, limited, region-specific, coarse-grained, overly aggregated, and inadequately calibrated. With the significant growth in the availability of time-series satellite imagery and derived products for exposure and hazard, we focus our work on the equally important yet challenging element of the risk equation: physical vulnerability. Given this unique problem, we leverage machine learning methods that flexibly capture spatial contextual relationships, limited temporal observations, and uncertainty in a unified probabilistic spatiotemporal inference framework. We therefore introduce Graph Variational State-Space Model ($\textbf{GraphVSSM}$), a novel modular spatiotemporal approach that uniquely integrates graph deep learning, state-space modeling, and variational inference using time-series data and prior expert belief systems in a weakly supervised or coarse-to-fine-grained manner. We present three major results: a city-wide demonstration in Quezon City, Philippines; an investigation of sudden changes in the cyclone-impacted coastal Khurushkul community (Bangladesh) and the mudslide-affected Freetown (Sierra Leone); and an open geospatial dataset, $\textbf{METEOR 2.5D}$, that spatiotemporally enhances the existing global static dataset for 46 UN-recognized Least Developed Countries (as of 2020). Beyond advancing the practice of regional disaster resilience assessment and improving our understanding of global progress in disaster risk reduction, our method also offers a probabilistic deep learning approach, contributing to broader urban studies that require compositional data analysis in weakly supervised settings.