  In this paper, we investigate cohomologies and non-abelian extensions of
lambda-weighted Rota-Baxter Lie coalgebras. First, we consider Lie comodules
and cohomologies of lambda-weighted Rota-Baxter Lie coalgebras. Next, we study
non-abelian extensions of lambda-weighted Rota-Baxter Lie coalgebras and
classify the non-abelian extensions in terms of non-abelian cohomology group.
Furthermore, we explore extensibility of a pair of automorphisms about a
non-abelian extension of lambda-weighted Rota-Baxter Lie coalgebras, and derive
the fundamental sequences of Wells in the context of lambda-weighted
Rota-Baxter Lie coalgebras. Finally, we discuss the previous results in the
case of abelian extensions of lambda-weighted Rota-Baxter Lie coalgebras.
