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We show that boundaries of 3D weak topological insulators can become gappedby strong interactions while preserving all symmetries, leading to Abeliansurface topological order. The anomalous nature of the weak topologicalinsulators manifests itself in a non-trivial action of symmetries on thequasiparticles; most strikingly, translations change the anyon types in amanner impossible in strictly 2D systems with the same symmetry. As a furtherconsequence, screw dislocations form non-Abelian defects that trap$\mathbb{Z}_4$ parafermion zero modes.

Anomalous Quasiparticle Symmetries and Non-Abelian Defects on Symmetrically Gapped Surfaces of Weak Topological Insulators