  Robustness of helical hinge states of three-dimensional weak second-order
topological i sulators (WSOTIs) against disorders is studied. The pure WSOTI is
obtained from a weak $\mathbb{Z}_2$ first-order topological insulator through a
surface band inversion. Both bulk states and surface states in the WSOTI are
gapped, and in-gap valley-momentum locked helical hinge states are
topologically protected by the surface valley-Chern number. In the presence of
weak disorders, helical hinge states are robust against disorders while the
quantized conductance of the states is fragile due to the inter-valley
scattering. As disorder increases, the system undergoes a series of quantum
phase transitions: from the WSOTI to the weak first-order topological
insulator, then to a diffusive metal and finally to an Anderson insulator. Our
results thus fully establish the WSOTI phase as a genuine state of matters and
open a door for the second-order valleytronics that allows one to control the
valley degree of freedom through helical hinge states.
