Distributing scarce spectral resources among the unlicensed users has been an attractive research area for Cognitive Radio Network's (CRN) research community. A resource distribution technique, which emphasizes fairness, ensures allocation of resources for all Secondary Users (SUs) irrespective of their data rates and may cause efficiency loss for the CRN. On the other hand, a throughput based resource allocation approach considers SUs with high data rates only and consequently SUs with low data rates face negative experiences as they starve from resources. Our work aims to balance between the fairness and the efficiency of a CRN. We formulate an objective function, which is a nonlinear convex function, to achieve maximum weighted sum rate for the SUs while ensuring fairness to all. We use Primal Dual Interior Point Method to solve the optimization problem and define a weight factor to obtain balance between the fairness and the throughput of the CRN. Finally we present an online iterative algorithm which maximizes the weighted sum rate of the SUs while guaranteeing QoS to the Primary Users (PUs). Numerical results exhibit that our method achieves higher throughput while ensuring adequate fairness to the SUs, compared to other traditional fairness schemes.