Due to limited energy resources, energy balancing becomes an appealing requirement/ challenge in Underwater Wireless Sensor Networks (UWSNs). In this paper, we present a Balanced Load Distribution (BLOAD) scheme to avoid energy holes created due to unbalanced energy consumption in UWSNs. Our proposed scheme prolongs the stability period and lifetime of the UWSNs. In BLOAD scheme, data (generated plus received) of underwater sensor nodes is divided into fractions. The transmission range of each sensor node is logically adjusted for evenly distributing the data fractions among the next hop neighbor nodes. Another distinct feature of BLOAD scheme is that each sensor node in the network sends a fraction of data directly to the sink by adjusting its transmission range and continuously reports data to the sink till its death even if an energy hole is created in its next hop region. We implement the BLOAD scheme, by varying the fractions of data using adjustable transmission ranges in homogeneous and heterogeneous simulation environments. Simulation results show that the BLOAD scheme outperforms the selected existing schemes in terms of stability period and network lifetime.