We present here a microscopic study of the effect of shear on a dense purely repulsive colloidal suspension. We use multispeckle diffusing wave spectroscopy to monitor the transient motions of colloidal particles after being submitted to an oscillatory strain. This technique proves efficient to record the time evolution of the distribution of relaxation times. After a high oscillatory shear, we show that this distribution displays full aging behavior. Conversely, when a moderate shear is applied the distribution is modified in a non-trivial way. Whereas high shear is able to erase all the sample history and rejuvenate it, a moderate shear helps it to age. We call this phenomenon overaging. We demonstrate that overaging can be understood if the complete shape of the relaxation time distribution is taken into account. We finally report how the soft glassy rheology model accounts for this effect.