  Let $\gcd(k,j)$ be the greatest common divisor of the integers $k$ and $j$.
For any arithmetical function $f$, we establish several asymptotic formulas for
weighted averages of gcd-sum functions with weight concerning logarithms, that
is $$\sum_{k\leq x}\frac{1}{k} \sum_{j=1}^{k}f(\gcd(k,j)) \log j.$$ More
precisely, we give asymptotic formulas for various multiplicative functions
such as $f=id$, $\phi$, $id_{1+a}$ and $\phi_{1+a}$ with $-1<a<0$. We also
establish some formulas of Dirichlet series having coefficients of the sum
function $\sum_{j=1}^{k}s_{k}(j)\log j$ where $s_{k}(j)$ is Anderson--Apostol
sums.
