Systemic racism can have broad impacts on health in ethnoracial minorities. One way is by suppressing socioeconomic status (SES) levels through barriers to achieve higher income, wealth, and educational attainment. Additionally, the weathering hypothesis proposes that the various stressful adversities faced by ethnoracial minorities lead to greater wear and tear on the body, known as allostatic load. In the present study, we extend these ideas to cognitive health in a tri-ethnic sample of young adults--when cognition and brain health is arguably at their peak. Specifically, we tested competing mediation models that might shed light on how two key factors caused by systemic racism--SES and perceived stress--intersect to explain ethnoracial disparities in cognition. We found evidence for partial mediation via a pathway from SES to stress on episodic memory, working memory capacity, and executive function in Black Americans relative to non-Hispanic White Americans. Additionally, we found that stress partially mediated the ethnoracial disparities in working memory updating for lower SES Black and Hispanic Americans relative to non-Hispanic White Americans, showing that higher SES can sometimes reduce the negative effects stress has on these disparities in some cognitive domains. Overall, these findings suggest that multiple pathways exist in which lower SES creates a stressful environment to impact ethnoracial disparities cognition. These pathways differ depending on the specific ethnoracial category and cognitive domain. The present results may offer insight into strategies to help mitigate the late-life risk for neurocognitive disorders in ethnoracial minorities.