  We describe the Aluthge transform of an unbounded weighted composition
operator acting in an $L^2$-space. We show that its closure is also a weighted
composition operator with the same symbol and a modified weight function. We
investigate its dense definiteness. We characterize $p$-hyponormality of
unbounded weighted composition operators and provide results on how it is
affected by the Aluthge transformation. We show that the only fixed points of
the Aluthge transformation on weighted composition operators are quasinormal
ones.
