  In this paper, we study the following class of weighted Choquard equations
  \begin{align*}
  -\Delta u =\lambda u + \Bigg(\displaystyle\int\limits_\Omega
\frac{Q(|y|)F(u(y))}{|x-y|^\mu}dy\Bigg) Q(|x|)f(u) ~~\textrm{in}~~ \Omega~~
\text{and}~~
  u=0~~ \textrm{on}~~ \partial \Omega,
  \end{align*}
  where $\Omega \subset \mathbb{R}^2$ is a bounded domain with smooth boundary,
$\mu \in (0,2)$ and $\lambda >0$ is a parameter. We assume that $f$ is a real
valued continuous function satisfying critical exponential growth in the
Trudinger-Moser sense, and $F$ is the primitive of $f$. Let $Q$ be a positive
real valued continuous weight, which can be singular at zero. Our main goal is
to prove the existence of a nontrivial solution for all parameter values except
the resonant case, i.e., when $\lambda$ coincides with any of the eigenvalues
of the operator $(-\Delta, H^1_0(\Omega))$.
