  In this paper, we first introduce the notion of a weighted
$\mathcal{O}$-operator on Hom-Lie triple systems with respect to an action on
another Hom-Lie triple system. Next, we construct a cohomology of weighted
$\mathcal{O}$-operator on Hom-Lie triple systems, we use the first cohomology
group to classify linear deformations and we investigate the obstruction class
of an extendable $n$-order deformation. We end this paper by introducing a new
algebraic structure, in connection with weighted $\mathcal{O}$-operators,
called Hom-post-Lie triple system. We further show that Hom-post-Lie triple
systems can be derived from Hom-post-Lie algebras.
