Abstract: The $k$-Weifeiler-Leman ($k$-WL) graph isomorphism test hierarchy is a common method for assessing the expressive power of graph neural networks (GNNs). Recently, the $2$-WL test was proven to be complete on weighted graphs which encode $3\mathrm{D}$ point cloud data. Consequently, GNNs whose expressive power is equivalent to the $2$-WL test are provably universal on point clouds. Yet, this result is limited to *invariant* continuous functions on point clouds.In this paper we extend this result in three ways: Firstly, we show that $2$-WL tests can be extended to point clouds which include both positions and velocity, a scenario often encountered in applications. Secondly, we show that PPGN can simulate $2$-WL *uniformly* on all point clouds with low complexity. Finally, we show that a simple modification of this *invariant* PPGN architecture can be used to obtain a universal *equivariant* architecture that can approximate all continuous equivariant functions uniformly.Building on our results, we develop our **WeLNet** architecture, which can process position-velocity pairs, compute functions fully equivariant to permutations and rigid motions, and is provably complete and universal. Remarkably, **WeLNet** is provably complete precisely in the setting in which it is implemented in practice. Our theoretical results are complemented by experiments showing **WeLNet** sets new state-of-the-art results on the N-Body dynamics task and the GEOM-QM9 molecular conformation generation task.