  In this paper, we use the Gauss Bonnet theorem to obtain the deflection angle
by the photons coupled to Weyl tensor in a Schwarzschild black hole and
Schwarzschild-like black hole in bumblebee gravity in the weak limit
approximation. To do so, we first calculate the corresponding optical metrics,
and then we find the Gaussian curvature to use in Gauss-Bonnet theorem, which
is first done by Gibbons and Werner. Hence, in the leading order terms we show
the deflection angle, that is affected by the coupling between the photon and
Weyl tensor, and there is a deviation from the deflecting angle as compared
with Schwarzschild black hole with Schwarzschild-like black hole in bumblebee
gravity. Moreover, we investigate the deflection angle by Einstein-Rosen type
wormhole in Weyl gravity and in bumblebee gravity. Interestingly, the
deflection angle by Einstein-Rosen type wormhole in bumblebee gravity is found
as larger than the the deflection angle by Einstein-Rosen type wormhole in Weyl
gravity.
