This paper investigates the problem of flow routing under interference constraints for wireless mesh networks. A new routing metric called cross-layer weight function CLWF, which is proved to be isotonic using virtual network decomposition, is initially developed by considering the traffic load and interference. Based on CLWF, a new routing algorithm called weighted hybrid multipath routing algorithm WHMRA is proposed in which the joint design of CLWF-based multipoint relay selection algorithm and fuzzy-slighted routing algorithm is introduced to improve the routing scalability. In addition, a cross-layer design framework is also developed in WHMRA in order to exchange information and enable interaction between layers where is enforced strict boundaries in original OSI networking model. Finally, through the system simulation and performance comparison, the proposed algorithms are demonstrated to succeed in improving network performance in terms of delay, packet loss ratio, throughput and overhead.