Studies on parochial altruism have insofar focused on the causes leading individuals to attack any outgroup on the behalf of one's group. Yet, we lack clues to understand why parochial altruists target specific groups, such as dominant groups in some contexts and minority groups in others. The present paper introduces an experiment to analyze the conditions under which individuals costly attack strong versus weak outgroups. In a first study, 300 participants played a repeated Inter-group Prisoner Dilemma involving multiple groups and inter-group differences in resources. Results show that individuals have a preference for targeting strong outgroups, but that attacks decrease when the inequality in destructive capacity between groups is high. Besides, individuals target weak outgroups when they are threatening their ingroup status. Decisions in the game correlate with participants' political ideology and Social Dominance Orientation. In a second study, we provide evidence that our results generalize to historical linkages between economic inequality and left-wing versus right-wing terrorist attacks.