  A two-dimensional spin-directed $\mathbb{Z}^{\,}_{2}$ network model is
constructed that describes the combined effects of dimerization and disorder
for the surface states of a weak three-dimensional $\mathbb{Z}^{\,}_{2}$
topological insulator. The network model consists of helical edge states of
two-dimensional layers of $\mathbb{Z}^{\,}_{2}$ topological insulators which
are coupled by time-reversal symmetric interlayer tunneling. It is argued that,
without dimerization of interlayer couplings, the network model has no
insulating phase for any disorder strength. However, a sufficiently strong
dimerization induces a transition from a metallic phase to an insulating phase.
The critical exponent $\nu$ for the diverging localization length at
metal-insulator transition points is obtained by finite-size scaling analysis
of numerical data from simulations of this network model. It is shown that the
phase transition belongs to the two-dimensional symplectic universality class
of Anderson transition.
