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In this paper, we introduce the notions of relative Rota-Baxter operators ofweight $1$ on Lie-Yamaguti algebras, and post-\LYA s, which is an underlyingalgebraic structure of relative Rota-Baxter operators of weight $1$. We givethe relationship between these two algebraic structures. Besides, we establishthe cohomology theory of relative Rota-Baxter operators of weight $1$ via theYamaguti cohomology. Consequently, we use this cohomology to characterizelinear deformations of relative Rota-Baxter operators of weight $1$ onLie-Yamaguti algebras. We show that if two linear deformations of a relativeRota-Baxter operator of weight $1$ are equivalent, then their infinitesimalsare in the same cohomology class in the first cohomology group. Moreover, weshow 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 theobstruction class in the second cohomology group is trivial.

Post Lie-Yamaguti algebras, relative Rota-Baxter operators of nonzero weights, and their deformations