  We propose classification schemes for characterizing two-dimensional
topological phases with nontrivial weak indices. Here, "weak" implies that the
Chern number in the corresponding phase is trivial, while the system shows edge
states along specific boundaries. As concrete examples, we analyze different
versions of the so-called Wilson-Dirac model with (i) anisotropic Wilson terms,
(ii) next nearest neighbor hopping terms, and (iii) a superlattice
generalization of the model, here in the tight-binding implementation. For
types (i) and (ii) a graphic classification of strong properties is
successfully generalized for classifying weak properties. As for type (iii),
weak properties are attributed to quantized Berry phase pi along a Wilson loop.
