A rigorous runtime analysis of evolutionary multi-objective optimization for the classical vertex cover problem in the context of parameterized complexity analysis has been presented by Kratsch and Neumann. In this paper, we extend the analysis to the weighted vertex cover problem and provide a fixed parameter evolutionary algorithm with respect to OPT, the cost of the optimal solution for the problem. Moreover, using a diversity mechanism, we present a multi-objective evolutionary algorithm that finds a 2−approximation in expected polynomial time.