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M-LWWF/M-LWDF scheduling schemes have attracted much interest due to their ability to both stabilize queues whenever possible and control delay through parameter selection. However, a good implementation of these schedulers would require a mechanism to minimize the required fraction of the bandwidth while satisfying its stability and delay requirements. To the best of our knowledge, previous works on these scheduling policies did not address the problem of minimizing the bandwidth utilization while satisfying delay constraints. In this paper, we explore the solution of this problem using a joint bandwidth and weight adaptation approach. We characterize the problem solution space for M-LWWF and M-LWDF scheduling, assuming time-varying traffic. We also show that, starting from any point in the solution space, simple dynamic bandwidth and weight updates can surely lead to the convergence to the optimal operation point in this space. Based on these characteristics, we propose a dynamic parameter adaptation algorithm that is able to track the time-varying optimal operation points for dynamic traffic and channel conditions. Simulation results show the efficiency of our proposed algorithm in tracking the optimal operation points in dynamic traffic and channel settings.