With the growing demand for device-free and privacy-preserving sensing solutions, Wi-Fi sensing has emerged as a promising approach for human pose estimation (HPE). However, existing methods often process vast amounts of channel state information (CSI) data directly, ultimately straining networking resources. This paper introduces TinySense, an efficient compression framework that enhances the scalability of Wi-Fi-based human sensing. Our approach is based on a new vector quantization-based generative adversarial network (VQGAN). Specifically, by leveraging a VQGAN-learned codebook, TinySense significantly reduces CSI data while maintaining the accuracy required for reliable HPE. To optimize compression, we employ the K-means algorithm to dynamically adjust compression bitrates to cluster a large-scale pre-trained codebook into smaller subsets. Furthermore, a Transformer model is incorporated to mitigate bitrate loss, enhancing robustness in unreliable networking conditions. We prototype TinySense on an experimental testbed using Jetson Nano and Raspberry Pi to measure latency and network resource use. Extensive results demonstrate that TinySense significantly outperforms state-of-the-art compression schemes, achieving up to 1.5x higher HPE accuracy score (PCK20) under the same compression rate. It also reduces latency and networking overhead, respectively, by up to 5x and 2.5x. The code repository is available online at here.