Capturing the past and present hydro-mechanical behavior of passive margin sediments raises noticeable interest, notably in geo-hazard risk assessment and hydrocarbon exploration. In this work, we aim at assessing the stress states undergone by these sedimentary deposits through geological time. To do so, we use an iterative coupling between a basin simulator and a finite element mechanical solver. This method conciliates a computation of the full stress tensors with a dynamic and geologically detailed modelling of the sedimentation. It is carried out on a dedicated set of 2D synthetic basin models, designed to be representative of siliciclastic deposition in passive margins and integrating variations in their geological history. Contrary to common assumptions in operational basin modelling studies, our results imply that passive margin sedimentary wedges are multidimensional mechanical systems, which endure significant non-vertical stress without external tectonic input. Our results also highlight the variability of the stress states through space and time, with a strong control from the geometry and lithological heterogeneities of the deposits. Lastly, we used the simulation results to predict a location and timing for the development of weakness zones in the sedimentary stacks, as privileged areas for rock failure. The outcome underlines the influence of the basal tilt angle, with a slight tilt impacting the wedges stability to a similar extent as a substantial increase in sedimentation rate. Altogether, this study emphasizes the need for careful consideration of non-vertical stresses in basin simulations, including in passive tectonic contexts. It also suggests that the iterative coupling method employed is a promising way to match industrial needs in this regard.