Background/Objectives: Obesity and insulin resistance (IR) increase the risk of mood disorders, which often manifest during young adulthood. However, neuroelectrophysiological investigations of whether adiposity and IR modify electrocortical activity and emotional processing outcomes remain underexplored, particularly in young adults. Therefore, this study used electroencephalography (EEG) to investigate whether obesity and/or IR moderate the relationships between brain potentials and affective processing in younger adults. Methods: Thirty younger adults completed a passive picture-viewing task utilizing the International Affective Picture System while real-time electroencephalography was simultaneously recorded. Two event-related potentials—early posterior negativity (EPN) and late positive potential (LPP)—were quantified. Affective processing parameters included mean valence ratings and stimulus-to-response-onset reaction times in response to unpleasant, pleasant, and neutral images. Body fat percentage and Homeostatic Model Assessment for Insulin Resistance values were measured. Hierarchical moderated regression analysis was utilized to test the interrelationships between brain potentials, adiposity, IR, and affective processing. Results: In the Negative−Neutral condition, lean and insulin-sensitive participants gave less negative valence ratings to unpleasant versus neutral images when late-window LPP amplitudes were larger, whereas this relationship was reversed in participants with obesity and absent in those with IR. Contrariwise, neither obesity nor IR moderated LPP responses to affective processing parameters in the Positive−Neutral or Negative−Positive valence conditions. Additionally, obesity and IR did not moderate the links between EPN responses and affective processing parameters in any of the valence conditions. Conclusions: Lean, insulin-sensitive young adults showed attenuated affective processing of unpleasant stimuli through stronger neural responses, whereas neural responses to pleasant stimuli did not vary across levels of body fat or IR. These preliminary findings suggest that both obesity and IR increase the vulnerability to mood disorders in young adulthood.