Ultra-wideband (UWB)-based techniques, while becoming mainstream approaches for high-accurate positioning, tend to be challenged by ranging bias in harsh environments. The emerging learning-based methods for error mitigation have shown great performance improvement via exploiting high semantic features from raw data. However, these methods rely heavily on fully labeled data, leading to a high cost for data acquisition. We present a learning framework based on weak supervision for UWB ranging error mitigation. Specifically, we propose a deep learning method based on the generalized expectation-maximization (GEM) algorithm for robust UWB ranging error mitigation under weak supervision. Such method integrate probabilistic modeling into the deep learning scheme, and adopt weakly supervised labels as prior information. Extensive experiments in various supervision scenarios illustrate the superiority of the proposed method.