This paper proposes a method for partitioning the vertex set of an undirected simple weighted graph into two subsets so as to minimise the difference of vertex-weight sums between the two subsets and the total weight of edges cut (i.e., edges with one end in each subset). The proposed heuristic algorithm works in a divide-and-conquer fashion and is a modification of an algorithm suggested in the literature. The algorithm has the same time complexity as the previous one but is extended to work on weighted graphs