Wireless Mesh Networks are mainly used for providing last-mile broadband wireless access. It is then highly recommended to ensure fairness among different users regardless of their physical locations while increasing their throughput. In this paper, we construct weighted contention graphs for the calculation of maximal capacity per flow and then we search how to maintain fairness per aggregate source-destination flow under bursty traffic. We propose a distributed dynamic contention window algorithm that uses an additional queue per node and we analytically show that our proposal can improve fairness in wireless mesh networks. We also show by simulations on OMNET++ the efficiency of the proposed solution even in bursty conditions. Thanks to the proposed solution, throughput capacity is much more fair compared to basic multihop networks.