The future Web of Things (WoT) foresees a web in which applications can seamlessly access physical objects through the same REST interface used today to access web services. A key enabler of this shift is the Constrained Application Protocol (CoAP), a redesign of the popular HTTP protocol that aims at supporting resource-constrained devices for Machine-to-Machine applications. In this work we propose a proxy virtualization framework to support scalability and easy implementation of custom functionalities in large WoT deployments. The functionalities offered by a CoAP proxy are exploited to transparently decouple applications from servers and to guarantee the implementation of custom policies and functionalities through virtualization techniques. A solution based on Linux Containers is implemented in a real test bed made of off-the-shelf hardware and open-source software, demonstrating the feasibility of the proposed design. Experimental results have shown that the response time is highly improved by our solution thanks to central coordination of concurrent requests from different virtual proxy instances. Moreover, to highlight the potential of the proposed frame-work, a priority-based Quality of Service policy is also implemented and evaluated.