  We consider weak topological insulators with a twofold rotation symmetry
around the dark direction, and show that these systems can be endowed with the
topological crystalline structure of a higher-order topological insulator
protected by rotation symmetry. These hybrid-order weak topological insulators
display surface Dirac cones on all surfaces. Translational symmetry breaking
perturbations gap the Dirac cones on the side surfaces leaving anomalous
helical hinge modes behind. We also prove that the existence of this
topological phase comes about due to a hidden crystalline topological invariant
of quantum spin-Hall insulators that can neither be revealed by symmetry
indicators nor using Wilson loop invariants. Considering the minimal symmetry
requirements, we anticipate that our findings could apply to a large number of
weak topological insulators.
