As the demand for mobile traffic is growing, radio frequency bandwidths often become insufficient for guaranteeing specific performance. Utilizing unlicensed 5 GHz broadband bandwidths, the LWA system enables the synergistic use of LTE and WiFi systems based on link aggregation techniques, without critical deterioration of service quality. This provides considerable benefits to the mobile operators when they successfully operate two networks and maintain an optimal balance in managing network resources. This study addresses balancing and fairness for newly emerging LWA systems. In particular, we develop a two-stage LWA access framework based on the Nash bargaining game. The framework further improves fairness and efficiency in the LTE-WiFi resource utilization by incorporating user segmentations on the basis of user characteristics, such as service contract and usage patterns. Extensive experiments using a network simulator with an NS-3 unlicensed band produce good performance in terms of fairness and efficiency. The proposed scheme demonstrates better outcomes compared to the existing methods while concurrently using radio resources in the LWA system in a fair manner. Moreover, our approach presents a simple and fast decision-making process and requires simple user profiles-contract status and traffic generation history. Therefore, the proposed scheme is far lighter and more flexible than traditional approaches that require extensive information exchanges between heterogeneous networks.