Weakly supervised video anomaly detection aims to detect anomalies and identify abnormal categories with only video-level labels. We propose CPL-VAD, a dual-branch framework with cross pseudo labeling. The binary anomaly detection branch focuses on snippet-level anomaly localization, while the category classification branch leverages vision-language alignment to recognize abnormal event categories. By exchanging pseudo labels, the two branches transfer complementary strengths, combining temporal precision with semantic discrimination. Experiments on XD-Violence and UCF-Crime demonstrate that CPL-VAD achieves state-of-the-art performance in both anomaly detection and abnormal category classification.