The IEEE802.11 wireless local-area network (WLAN) has been extensively deployed as inexpensive and flexible Internet access services. We have studied the elastic WLAN system that dynamically optimizes the network configuration depending on traffic demands. Our testbed experiments using Raspberry Pi revealed that concurrent TCP communications of multiple hosts with a single AP cause the unfairness in throughput performances. In this paper, we propose the TCP fairness control method for two-host concurrent communications. The delay is introduced in the AP at the packet transmissions to the faster host, to increase transmission opportunities with the slower host. The delay is initially estimated by the received signal strength (RSS) from each host, and then, is dynamically optimized using the PI controller. For evaluations, we implement the proposal in the elastic WLAN system testbed, and conduct extensive experiments, where the TCP throughput fairness is achieved.