  We derive the spin texture of a weak topological insulator via a
supersymmetric approach that includes the roles of the bulk gap edge states and
surface band bending. We find the spin texture can take one of four forms: (i)
helical, (ii) hyperbolic, (iii) hedgehog, with spins normal to the Dirac-Weyl
cone of the surface state, and (iv) hyperbolic hedgehog. Band bending
determines the winding number in the case of a helical texture, and for all
textures can be used to tune the spin texture polarization to zero. For the
weak topological insulator SnTe, we show that inclusion of band bending is
crucial to obtain the correct texture winding number for the (111) surface
facet $\Gamma$-point Dirac-Weyl cone. We argue that hedgehogs will be found
only in low symmetry situations.
