Coverage path planning (CPP) is the problem of determining a path that covers any given area and is mainly applied in the field of robotics. To ensure efficient coverage, objectives like path length, overlaps, and traversal time are considered. However, in certain scenarios, a simplistic total coverage approach may not be optimal, necessitating a trade-off strategy. This paper addresses a novel challenge in CPP: the multi-objective weighted coverage path planning problem, where total coverage is not strictly required but balanced against other objectives and constraints. We present an approach to solve this problem using evolutionary multi-objective algorithms with free-form path representations. The focus lies on comparing different path representations, ranging from polygonal chains to Bézier curves and B-splines, to Non-Uniform Rational B-splines (NURBs). Additionally, we incorporate an overlaid rectangular grid for comparison with a graph-based approach.