Lifetime extension is a critical issue for wireless body area network (WBAN) with limited battery energy. Unlike common wireless sensor network (WSN), sensor nodes' data rate requirements are heterogeneous in WBAN. Fairness assurance is also indispensable to avoid the consequence that a certain sensor node fails to be scheduled for a long time when the channel condition is persistently severe. With constrained battery energy, increasing network lifetime and maintaining fairness are conflicting performance metrics. For this reason, a new distributed transmission scheduling scheme called fair weights scheme is proposed in this paper to balance lifetime and fairness. Apart from channel state information (CSI) and residual energy information (REI), data rates requirements of sensor nodes are crucial in this scheme. Simulation results show that the fair weights scheme can effectively allocate time slots to balance lifetime and fairness performance in various channel conditions.