  This paper aims to investigate the thermodynamic formalism of weighted
amenable topological pressure for factor maps of amenable group actions.
Following the approach of Tsukamoto [\emph{Ergodic Theory Dynam. Syst.}
\textbf{43}(2023), 1004-1034.], we introduce the notion of weighted amenable
topological pressure for factor maps of amenable group actions, and establish a
variational principle for it. As the application of variational principle, we
show weighted amenable measure-theoretic entropy can be determined by weighted
amenable topological pressure. Equilibrium states of weighted topological
pressure are also involved.
