Human activity recognition (HAR) based on WiFi channel state information (CSI) has received a lot of attentions recently due to its non-intrusive nature. Most CSI-based HAR systems use a WiFi router and a computing terminal for centralized processing, which makes it difficult to achieve real-time wide-range recognition. Recently, lightweight artificial intelligence internet of things (AIoT) devices are widely deployed. The equipped WiFi chips within such devices can collect and process CSI data in a distributed way. Thus, the AIoT devices extend the detection range of collecting CSI and enrich the applications. However, the memories of the AIoT devices are constrained and lack of appropriate lightweight CSI processing strategies. To address these challenges, we propose the LiWi-HAR system which employs a comprehensive lightweight CSI processing strategy in WiFi based AIoT devices. The proposed lightweight CSI processing strategy extracts the main related features while compressing the data size. Then, a double hidden layer BP neural network based on particle swarm optimization (PSO-BPNN) algorithm is developed for HAR. In this case, the computing memory occupation of the device is effectively reduced, and the real-time high accurate recognition is achieved. Extensive experimental results present that the efficiency of our system significantly outperforms other centralized deep learning based systems and the recognition accuracy achieves 91.7%.