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In wireless networks where all users have different channel characteristics and service classes, it is challenging to design an adaptive scheduler to support quality of service (QoS). Some fraction of multiuser diversity gain, which offers significant capacity increase, should be sacrificed to meet certain QoS targets. We present an opportunistic scheduling scheme under resource-sharing constraints. The scheduler solves the weighted fairness by diverting a fraction of resources from surplus users to underserved users. Given the average received signal-to-noise ratios (SNR) of users and resource-sharing constraints, the capacity of the proposed scheduler is analyzed over Rayleigh fading channels. Degree of weighted fairness for various scheduling schemes is also provided. Numerical results illustrate that while sacrificing a fraction of the achievable total capacity the proposed scheduler provides perfect weighted fairness.