Following the huge commercial success of WLAN, multihop wireless networks are expected to lead in the next wave of deployment. Fundamental methods for traffic engineering must be developed to support diverse application requirements in these networks. This paper studies the problem of how to support weighted bandwidth allocation among all end-to-end flows in a multihop wireless network. Our goal is to enable the network to adapt the flow rates such that global maxmin can be achieved. Our approach is to transform the global maxmin objective into four local conditions and design a distributed rate adaptation protocol based on those local conditions. Comparing with the prior art, our protocol has a number of advantages. It is designed for the popular IEEE 802.11 DCF. It replaces per-flow queueing with per-destination queueing. It achieves far better fairness (or weighted fairness) among end-to-end flows.