WiFi-based human activity recognition (HAR) holds significant promise for ubiquitous sensing in smart environments. A critical challenge lies in enabling systems to dynamically adapt to evolving scenarios, learning new activities without catastrophic forgetting of prior knowledge, while adhering to the stringent computational constraints of edge devices. Current approaches struggle to reconcile these requirements due to prohibitive storage demands for retaining historical data and inefficient parameter utilization. We propose WECAR, an end-edge collaborative inference and training framework for WiFi-based continuous HAR, which decouples computational workloads to overcome these limitations. In this framework, edge devices handle model training, lightweight optimization, and updates, while end devices perform efficient inference. WECAR introduces two key innovations, i.e., dynamic continual learning with parameter efficiency and hierarchical distillation for end deployment. For the former, we propose a transformer-based architecture enhanced by task-specific dynamic model expansion and stability-aware selective retraining. For the latter, we propose a dual-phase distillation mechanism that includes multi-head self-attention relation distillation and prefix relation distillation. We implement WECAR based on heterogeneous hardware using Jetson Nano as edge devices and the ESP32 as end devices, respectively. Our experiments across three public WiFi datasets reveal that WECAR not only outperforms several state-of-the-art methods in performance and parameter efficiency, but also achieves a substantial reduction in the model's parameter count post-optimization without sacrificing accuracy. This validates its practicality for resource-constrained environments.