Wireless mesh network (WMN) is a practical and cost effective solution for home and business networks. However, in multi-hop wireless mesh networks, the throughput decays significantly with an increase in hop counts. This is primarily due to the increase in successive spatial contentions. As a result, flows with longer hops from the gateway suffer from bandwidth starvation and fair link access disparities. In this paper, we show that the packet size and the minimum contention window size (CW) play an essential role in improving fairness in multi-hop WMNs. Based on their location in the network and their traffic load; nodes may adapt different packet sizes and various CWs to improve their throughput. We present a Fair Share Algorithm (FSA) that assists each node in computing a fair packet size and a fair CW. We demonstrate that the FSA accomplishes considerably better fairness with minimal negative affect on the overall system throughput. The algorithm results are evaluated and compared with the performance of the default IEEE 802.11 MAC protocol used in wireless mesh networks.