Scientific attention is unevenly distributed, creating inequities in recognition and distorting access to opportunities. Using citations as a proxy, we quantify disparities in attention by gender and institutional prestige. We find that women receive systematically fewer citations than men, and that attention is increasingly concentrated among authors from elite institutions -- patterns not fully explained by underrepresentation alone. To explain these dynamics, we introduce a model of citation network growth that incorporates homophily (tendency to cite similar authors), preferential attachment (favoring highly cited authors) and group size (underrepresentation). The model shows that disparities arise not only from group size imbalances but also from cumulative advantage amplifying biased citation preferences. Importantly, increasing representation alone is often insufficient to reduce disparities. Effective strategies should also include reducing homophily, amplifying the visibility of underrepresented groups, and supporting equitable integration of newcomers. Our findings highlight the challenges of mitigating inequities in asymmetric networks like citations, where recognition flows in one direction. By making visible the mechanisms through which attention is distributed, we contribute to efforts toward a more responsible web of science that is fairer, more transparent, and more inclusive, and that better sustains innovation and knowledge production.