Let gcd (k, j) be the greatest common divisor of the integers k and j. We establish some asymptotic formulas for weighted averages of the gcd-sum functions, that is Sigma(k <= x) 1/k(r+1) Sigma(k)(j=1) j(T) f (gcd(k, j)) with f = id, phi,phi(s), psi and psi(s) for any fixed positive integers r and s, where phi,phi(s), psi and psi(s) and are the Euler, the Jordan, the Dedekind and the generalized Dedekind function, respectively, and also prove the mean square formulas of the gcd-sum function Sigma(k <= x) 1/k(r+1). Sigma(k)(j=1) j(r) phi(gcd(k,j)) and Sigma(k <= x) 1/k(r+1) Sigma(k)(j=1) j(r) psi(gcd(k,j)). (C) 2017 Published by Elsevier Inc.