In 2019, a new selection method, named fitness-distance balance (FDB), was proposed. FDB has been proved to have a significant effect on improving the search capability for evolutionary algorithms. But it still suffers from poor flexibility when encountering various optimization problems. To address this issue, we propose a functional weights-enhanced FDB (FW). These functional weights change the original weights in FDB from fixed values to randomly generated ones by a distribution function, thereby enabling the algorithm to select more suitable individuals during the search. As a case study, FW is incorporated into the spherical search algorithm. Experimental results based on various IEEE CEC2017 benchmark functions demonstrate the effectiveness of FW.