In this paper, we present a proxy-based solution for adapting the scalable video streams at the edge of a wireless network, which can respond quickly to highly dynamic wireless links. Our design adopts the scalable video coding (SVC) technique for lightweight rate adaptation at the edge. We derive a QoE model, i.e., rate-quality tradeoff model, that relates the maximum subjective quality under a given rate by choosing the optimal frame rate and quantization stepsize. The proxy iteratively allocates rates of different video streams to maximize a weighted sum of video qualities associated with different streams, based on the periodically observed link throughputs and the sending buffer status. Simulation studies show that our scheme consistently outperforms TFRC in terms of agility to track link qualities and overall quality of all streams. In addition, the proposed scheme supports differential services for different streams, and competes fairly with TCP flows.