For a weight \(\mu \) , that is, a positive continuous function defined on the open unit disk \(\mathbb {D}\) in \(\mathbb {C}\) , the weighted harmonic Bloch-type space \(\mathcal {B}^\mu _H\) is the collection of the complex-valued harmonic mappings f defined on \(\mathbb {D}\) such that \(\Vert f\Vert _{\mathcal {B}_H^\mu }{:}{=}|f(0)|+\sup _{z\in \mathbb {D}}\mu (z)\big (|f_z(z)|+|f_{\overline{z}}(z)|\big )<\infty ,\) where \(f_z\) and \(f_{\overline{z}}\) denote the first complex partial derivatives with respect to z and \(\overline{z}\) . In this work, given an analytic self-map, \(\varphi \) , of \(\mathbb {D}\) , and a weight \(\mu \) , we characterize the bounded and the compact composition operators \(C_\varphi \) from a class of Banach spaces X of harmonic mappings on \(\mathbb {D}\) into the weighted harmonic Bloch-type space \(\mathcal {B}^\mu _H\) . We study in detail the composition operator between the harmonic Bloch-type spaces \(\mathcal {B}^\alpha _H\) and \(\mathcal {B}^\beta _H\) whose corresponding weights are \((1-|z|^2)^\alpha \) and \((1-|z|^2)^\beta \) , where \(\alpha ,\beta >0\) . In particular, we give an approximation of the operator norm and obtain a precise formula when the symbol fixes the origin. We extend some results on the isometries among such operators that are valid on the corresponding subspaces of analytic functions. Furthermore, we provide a formula of the essential norm in terms of the norm of the monomials \(z^k\) and their corresponding images \(\varphi ^k\) under the operator.
