[Objective] Due to insufficient measurement devices, the observability of distribution networks is relatively poor, which undermines the accuracy of state estimation. To address this issue, this paper proposes a prior-enhanced state estimation method for weakly observable distribution networks based on dynamic partitioning, which enables full-node state estimation utilizing measurements from observable areas. [Methods] First, node observability analysis and real-time dynamic partitioning are performed in accordance with the available measurement data. On this basis, a regional state mapping model is constructed to realize real-time state estimation in unobservable areas. Second, leveraging the prior state information from historical system states, a prediction error covariance matrix is formulated to establish a prior-enhanced extended Kalman filter (PEEKF) model. This method avoids updating the error covariance during posterior estimation, thereby improving estimation efficiency while maintaining accurate estimation states in the observable areas. Finally, the states of observable areas are mapped to the states of unobservable areas through the state mapping model, yielding the state estimates for the unobservable areas of the distribution networks. [Results] Simulation tests are conducted on the IEEE 33-node and 95-node systems. The average absolute percentage error of the algorithm remains consistently below 0.4% in both systems. Compared with the Extended Kalman Filter, Unscented Kalman Filter, and Adaptive Interpolation Kalman Filter, the proposed method achieves significantly higher estimation accuracy. [Conclusions] The proposed method can effectively perform dynamic partitioning and state mapping, and achieve high real-time and high-precision state tracking of weakly observable distribution networks.