In this paper, by applying the accurate estimates of the Hörmander class, the authors consider the commutators of bilinear pseudo-differential operators and the operation of multiplication by a Lipschitz function. By establishing the pointwise estimates of the corresponding sharp maximal function, the boundedness of the commutators is obtained respectively on the products of weighted Lebesgue spaces and variable exponent Lebesgue spaces with $\sigma \in \mathcal{B}B{S}_{1,1}^1$. Moreover, the endpoint estimate of the commutators is also established on $L^{\mathrm{\infty }}\times L^{\mathrm{\infty }}$.

The main purpose of this paper is to establish the weighted boundedness result of vector valued bilinear $\varpi (t)$-type Calderón-Zygmund operators in variable exponents Herz-Morrey spaces, where $\varpi$ being nondecreasing and $\varpi \in \mathrm{D}\mathrm{i}\mathrm{n}\mathrm{i}(1)$.