In property insurance claims triage, insurers often use static information to assess the severity of a claim and identify the subsequent actions. We hypothesize that the pattern of weather conditions throughout the course of the loss event is predictive of insured losses and hence appropriate use of weather dynamics improve the operation of insurer's claim management. To test this hypothesis, we propose a deep learning method to incorporate the dynamic weather data in the predictive modeling of insured losses for reported claims. The proposed method features a hierarchical network architecture to address the challenges introduced into claims triage by weather dynamics. In the empirical analysis, we examine a portfolio of hail damage property insurance claims obtained from a major U.S. insurance carrier. When supplemented by the dynamic weather information, the deep learning method exhibits substantial improvement in the hold-out redictive performance.