We propose, in this paper, a novel approach of Access Point (AP) backhaul capacity aggregation in the context of Wireless Local Area Networks (WLAN). Our purpose is to optimize the Available Backhaul Resource (ABR) allocation between APs belonging to different Basic Service Sets (BSSs), so as to relieve pressure of traffic offloaded from non-WiFi networks. In this context, we define two different sets of APs within the same WLAN: the ones with spare backhaul resources (Providers) and those in lack of it (Beneficiaries). Considering the two sided nature of this system, we model our assignment problem using matching games: one-to-one, many-to-one and many-to-many, and solve it using the so-called Deferred Acceptance (DA) algorithm leading to an optimal pairwise stable matching. Our results show that, compared to a legacy WLAN, the overall performance is substantially improved in terms of AP throughput gain, AP satisfaction percentage and load balancing between different APs