  Using Monte Carlo simulations, we have studied isothermal aging of
three-dimensional Ising spin-glass model focusing on quasi-equilibrium behavior
of the spin auto-correlation function. Weak violation of the time translational
invariance in the quasi-equilibrium regime is analyzed in terms of {\it
effective stiffness} for droplet excitations in the presence of domain walls.
Within the range of computational time window, we have confirmed that the
effective stiffness follows the expected scaling behavior with respect to the
characteristic length scales associated with droplet excitations and domain
walls, whose growth law has been extracted from our simulated data. Implication
of the results are discussed in relation to experimental works on ac
susceptibilities.
