This paper is concerned with the influence of apparatus inertia effects in controlled stress rheometry. As evidenced on creep experiments, the coexistence of apparatus inertia and viscoelasticity leads to a coupling frequency. For weak gels, this coupling frequency is typically between 1 and 100 Hz. Therefore, frequency sweeps around and above this coupling frequency also corresponds to an effective shear stress sweep evolution due to a non-trivial resonant effect. In other words, frequency sweep experiments are not made at constant shear stress. The detailed modelling and analysis of this inertia effect on a typical weak gel shows a clear and fundamental limitation for its characterization using a controlled stress rheometer. Also, alternative approaches to standard rheometer software analysis are proposed to take this coupling effect into account.