Mobile Edge Computing (MEC) provides the radio access networks with cloud computing capabilities to fulfill the requirements of the Internet of Things (IoT) services such as high reliability and low latency. Offloading services to edge servers can alleviate the storage and computing limitations and prolong the lifetimes of the IoT devices. However, offloading in MEC faces scalability problems due to the massive number of IoT devices. In this article, we present a new integration architecture of the cloud, MEC and IoT, and propose a lightweight request and admission framework to resolve the scalability problem. Without coordination among devices, the proposed framework can be operated at the IoT devices and computing servers separately, by encapsulating latency requirements in offloading requests. Then, a selective offloading scheme is designed to minimize the energy consumption of devices, where the signalling overhead can be further reduced by enabling the devices to be selfnominated or self-denied for offloading. Simulation results show that our proposed selective offloading scheme can satisfy the latency requirements of different services and reduce the energy consumption of the IoT devices.