We classify solutions of the vacuum weighted Einstein field equations on smooth metric measure spacetimes \((M,\mathsf {g},h\, dvol_g)\) of dimension 4, where the underlying manifold \((M,\mathsf {g})\) is a pr-wave. We use this result to provide examples of solutions with some special geometric properties. The gradient \(\nabla h\) is lightlike or spacelike. In the first case, the underlying manifold is a pp-wave. In the second case, the Ricci operator is either 2- or 3-step nilpotent. Moreover, 2-step nilpotent solutions are also realized on pp-waves.