This paper proposes an energy aware and bandwidth efficient mobility support architecture which handles mobility of 6LoWPAN devices, such that the communication between it and its corresponding nodes remain undisrupted. As the 6LoWPAN devices are energy and resource constrained enabling mobility in these devices with the help of conventional Host Based protocols like MIPv6 is not suitable. Moreover, it may be possible in many scenarios that the Mobile Node (MN) moves far from the Gateway (GW), while communicating with it. In this case the MN has to increase its transmission power, which may adversely affect its life time. In the proposed architecture static random deployed 6LoWPAN devices (SN) with same characteristics as the MNs, facilitate mobility such that the IP connectivity of the MN is maintained with minimum signaling at MN's end. Thus this paper describes the link layer specific mechanisms needed between the SN and the MN to help it perform multi-hop communication with the GW. Moreover, it is designed keeping in mind the energy and resource constraint nature of SNs themselves. The signaling overhead for the SNs is determined through analytical modeling.