In two-way relay network (TWRN), end nodes may have different quality-of-service (QoS) requirements according to their priority, traffic demand, and/or their downlink and uplink split ratio. In this paper, the heterogeneity among network users that have different traffic load/demands is considered by assuming a weighted fairness between the two end nodes. An energy efficient design is proposed for two-way relaying (TWR) with time division broadcast (TDBC) protocol that minimizes the allocated power to the two transceivers and the relay node under a weighted quality-of-service (QoS) bidirectional data rates requirement with weighting factor (a). This design utilizes the signal combining process at the relay node in TDBC, also known as relay power allocation (RPA), to provide a new simpler way to ensure the weighted rates without increasing the complexity to control different power allocation of the three nodes. Adaptive calculation of the relay power allocation factor, e, is adopted for combining the two received signals to satisfy the QoS requirements. Simulation results show an improvement in the efficiency in terms of the average allocated power and an improved users' fairness compared with scenarios where a predetermined fixed value of e is used.