An orientation of an undirected graph G has weak diameter k if, for every pair {u, v} of vertices of G, there is a directed path with length at most k joining u and v in either direction. We show that deciding whether an undirected graph admits an orientation with weak diameter k is NP-complete for every k ≥ 2. This result implies the NP-completeness of deciding whether an undirected graph can be turned into the analogue of a clique for proper colouring of several augmented kinds of graphs.