  In this paper, we introduce the notions of relative Rota-Baxter operators of
weight $1$ on Lie-Yamaguti algebras, and post-\LYA s, which is an underlying
algebraic structure of relative Rota-Baxter operators of weight $1$. We give
the relationship between these two algebraic structures. Besides, we establish
the cohomology theory of relative Rota-Baxter operators of weight $1$ via the
Yamaguti cohomology. Consequently, we use this cohomology to characterize
linear deformations of relative Rota-Baxter operators of weight $1$ on
Lie-Yamaguti algebras. We show that if two linear deformations of a relative
Rota-Baxter operator of weight $1$ are equivalent, then their infinitesimals
are in the same cohomology class in the first cohomology group. Moreover, we
show that an order $n$ deformation of a relative Rota-Baxter operator of weight
$1$ can be extended to an order $n+1$ deformation if and only if the
obstruction class in the second cohomology group is trivial.
