We consider the 1∣∣∑ w_jU_j problem, the problem of minimizing the weighted number of tardy jobs on a single machine. This problem is one of the most basic and fundamental problems in scheduling theory, with several different applications both in theory and practice. Using a reduction from the Multicolored Clique problem, we prove that 1∣∣∑ w_jU_j is W[1]-hard with respect to the number p_# of different processing times in the input, as well as with respect to the number w_# of different weights in the input. This, along with previous work, provides a complete picture for 1∣∣∑ w_jU_j from the perspective of parameterized complexity, as well as almost tight complexity bounds for the problem under the Exponential Time Hypothesis (ETH).