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Optimal use of genetics for precision medicine requires polygenic scores (PGS) that predict not just risk of disease, but also response to pharmaceutical or lifestyle interventions. These are detectable in observational datasets as PGS-by-exposure (PGS×E) interactions. Existing literature suggests that PGS based on interactions (iPGS) or variance effects (vPGS) may be more powerful than standard marginal PGS (mPGS) for the detection of PGS×E, but these have yet to be systematically compared. We describe a generalized pipeline for the development and comparison of different PGS types and apply it to detect genetic modification of the relationship between adiposity (measured by body mass index [BMI]) and a broad set of cardiometabolic risk factors (CRFs). Our applied analysis in the UK Biobank cohort identified significant PGS×BMI for at least one PGS type for 16/20 of these CRFs, many of which replicated in the All of Us cohort. Among PGS types, iPGS uncovered interactions with BMI most consistently across CRFs, with the strongest interactions impacting biomarkers of liver function (e.g., alanine aminotransferase [ALT]). Exploring the ALT iPGS more in-depth, we find a substantial effect modification of up to 72% larger BMI-ALT association in the top iPGS decile in All of Us, and further provide evidence that the iPGS prioritizes variants affecting hepatic lipid export. Taken together, our study provides a framework for the development and comparison of PGS×E strategies, quantifies genetic impacts on the adiposity-cardiometabolic risk relationship, and informs efforts to move toward clinically useful response-focused PGS.