We report a detailed experimental study of the aging of the (initial) random hexagonal close-packed (rhcp) crystals formed in suspensions of hard-sphere colloids near the melting point. By suspending the same colloidal particles in two different mixtures of solvents we are able to tune the strength of the gravitational forces acting on the particles. The crystal structure is deduced from diffraction patterns measured by the light scattering equivalent of powder x-ray crystallography. A spontaneous aging of the structure is observed over long periods of time, consisting of a fraction of pure face-centered cubic (fcc) crystals growing at the expense of the randomly stacked crystallites. The rate of growth of the new crystals is small and consistent with the predictions by Pronk and Frenkel [13]. Gravity is also revealed to affect the crystals and favor fcc order but through a slow gradual rearrangement of the random stacking. An important new observation is that small mechanical perturbations can strongly affect the structure of the colloidal crystals, promoting fcc growth and interfering with the spontaneous aging process. Previous experimental results are also discussed in the light of these new findings.