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Abstract Weighting methods are popular tools for estimating causal effects, and assessing their robustness under unobserved confounding is important in practice. Current approaches to sensitivity analyses rely on bounding a worst-case error from omitting a confounder. In this paper, we introduce a new sensitivity model called the variance-based sensitivity model, which instead bounds the distributional differences that arise in the weights from omitting a confounder. The variance-based sensitivity model can be parameterized by an R2 parameter that is both standardized and bounded. We demonstrate, both empirically and theoretically, that the variance-based sensitivity model provides improvements on the stability of the sensitivity analysis procedure over existing methods. We show that by moving away from worst-case bounds, we are able to obtain more interpretable and informative bounds. We illustrate our proposed approach on a study examining blood mercury levels using the National Health and Nutrition Examination Survey.