Polygenic scores (PGS) are now commonly available in longitudinal cohort studies, leading to their integration into epidemiological research. In this work, our aim is to explore how polygenic scores can be used as exposures in causal inference-based methods, specifically mediation analyses. We propose to estimate the extent to which the association of a polygenic score indexing genetic liability to an outcome could be mitigated by a potential intervention on a mediator. To do this this, we use the interventional disparity measure approach, which allows us to compare the adjusted total effect of an exposure on an outcome, with the association that would remain had we intervened on a potentially modifiable mediator. As an example, we analyse data from two UK cohorts, the Millennium Cohort Study (MCS, N = 2575) and the Avon Longitudinal Study of Parents and Children (ALSPAC, N = 3347). In both, the exposure is genetic liability for obesity (indicated by a PGS for BMI), the outcome is late childhood/early adolescent BMI, and the mediator and potential intervention target is physical activity, measured between exposure and outcome. Our results suggest that a potential intervention on child physical activity can mitigate some of the genetic liability for childhood obesity. We propose that including PGSs in a health disparity measure approach, and causal inference-based methods more broadly, is a valuable addition to the study of gene-environment interplay in complex health outcomes.