Background/Objectives: Obesity and insulin resistance (IR) increase the risk for mood disorders and may impair emotional experiences. This study investigated whether obesity and/or IR moderated the links between brain potentials and affective processing during young adulthood. Methods: Thirty young adults completed a passive picture-viewing task utilizing the International Affective Picture System while real-time electroencephalography was simultaneously recorded. Two event-related potential components—early posterior negativity (EPN) and late positive potential (LPP)—were quantified. Affective processing parameters included the 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 parameters. Results: In the Negative–Neutral valence condition, lean and insulin-sensitive participants gave less negative valence ratings to unpleasant versus neutral images when late-window LPP amplitudes were larger, whereas respective counterparts showed no such relationship. Contrariwise, obesity and IR did not moderate the links between LPP amplitudes and affective processing parameters in the Positive–Neutral or Negative–Positive conditions. Additionally, EPN amplitudes and affective processing scores were not moderated by obesity or IR across any of the valence conditions. Conclusions: Lean and insulin-sensitive young adults showed attenuated negative affective processing of unpleasant versus neutral stimuli through increased brain activity, whereas obese and insulin-resistant young adults did not. In contrast, obesity and IR did not modify the relationship between neural activity and positive affective processing in young adults.