Covering a given area with a team of mobile robots in a minimum time is a well-studied problem with many real-world applications. A rarely studied subject, however, is the case of a weighted plane: due to the necessity of taking time-consuming measurements or having to traverse different kinds of terrains, the coverage time may vary over the environment and the path planning needs to be adapted accordingly. In this paper, we present an adapted version of a state-of-the-art mCPP (multi-robot coverage path planning) approach, the DARP algorithm, to make it suitable to deal with weighted environments. In particular, we propose several modifications to DARP that allow overcoming some of its limitations and, as a result, obtain an increased convergence rate and decreased convergence time with respect to the original version. Furthermore, as proved by extensive simulations, these improvements are also noticed in the unweighted version of the problem.