  In this paper, we study hyponormal weighed composition operators on the Hardy
and weighted Bergman spaces. For functions $\psi \in A(\mathbb{D})$ which are
not the zero function, we characterize all hyponormal compact weighted
composition operators $C_{\psi,\varphi}$ on $H^{2}$ and $A^{2}_{\alpha}$. Next,
we show that for $\varphi \in \mbox{LFT}(\mathbb{D})$, if $C_{\varphi}$ is
hyponormal on $H^{2}$ or $A^{2}_{\alpha}$, then $\varphi(z)=\lambda z$, where
$|\lambda| \leq 1$ or $\varphi$ is a hyperbolic non-automorphism with
$\varphi(0)=0$ and such that $\varphi$ has another fixed point in $\partial
\mathbb{D}$. After that, we find the essential spectral radius of $C_{\varphi}$
on $H^{2}$ and $A^{2}_{\alpha}$, when $\varphi$ has a Denjoy-Wolff point $\zeta
\in \partial \mathbb{D}$. Finally, descriptions of spectral radii are provided
for some hyponormal weighted composition operators on $H^{2}$ and
$A^{2}_{\alpha}$.
