A network can be structurally controlled by attaching driver nodes to some of its vertices. We look at real networks with weighted edges and iteratively cut edges to study how the number N_D of driver nodes needed to fully control the network varies. We find that targeting lighter / heavier edges, compared to targeting random edges, consistently yields a slower or faster increase in the number N_D, depending on how the edge weights correlate with topological features such as node degrees. We also study the variation of the control profile during the thresholding process.