This paper investigates the sinks mobility in IPv6- based wireless sensors networks and specially in the new IETF proposed protocol RPL (Routing Protocol for Low power and Lossy Networks). We also show that even the mobility of sinks is not an explicit design criteria, the use of mobile sinks improves the network lifetime. In this work, we propose a new distributed and weighted moving strategy for sinks in RPL. We compared our proposed mobility approach with different others strategies. The results show that our proposed mobility approach notably balances the network load which leads to a significant network lifetime gain in large scale network.