  We report the experimental realization of two-dimensional (2D) weak
topological insulator (WTI) in spinless Su-Schrieffer-Heeger circuits with
parity-time and chiral symmetries. Strong and weak $\mathbb{Z}_2$ topological
indexes are adopted to explain the experimental findings that a Dirac semimetal
(DSM) phase and four WTI phases emerge in turn when we modulate the
centrosymmetric circuit deformations. In DSM phase, it is found that the Dirac
cone is highly anisotropic and not pinned to any high-symmetry points but can
widely move within the Brillouin zone, which eventually leads to the phase
transition between WTIs. In addition, we observe a pair of flat-band domain
wall states by designing spatially inhomogeneous node connections. Our work
provides the first experimental evidence for 2D WTIs, which significantly
advances our understanding on the strong and weak nature of topological
insulators, the robustness of flat bands, and the itinerant and anisotropic
feature of Dirac cones.
