  While strong topological insulators (STI) have been experimentally realized
soon after their theoretical predictions, a weak topological insulator (WTI)
has yet to be unambiguously confirmed. A major obstacle is the lack of distinct
natural cleavage surfaces to test the surface selective hallmark of WTI. With a
new scheme, we discover that Bi$_{4}$X$_{4}$ (X=Br, I), stable or synthesized
before, can be WTI with two natural cleavage surfaces, where two anisotropic
Dirac cones stabilize and annihilate, respectively. We further find four
surface state Lifshitz transitions under charge doping and two bulk topological
phase transitions under uniaxial strain. Near the WTI-STI transition, there
emerges a novel Weyl semimetal phase, in which the Fermi arcs generically
appear at both cleavage surfaces whereas the Fermi circle only appears at one
selected surface.
