Size-based dominance hierarchies influence fitness, group size and population dynamics and link dominance structure to evolutionary and ecological outcomes. While larger individuals often gain dominance, social status may influence growth and size in return, resulting in feedbacks among status, growth and size. Here, we present two models evaluating how these feedbacks influence the emergence of size structure in a dominance hierarchy. In the first, size influences competition for food and investment in suppressing growth of groupmates. Stable size differences emerged when suppression was greatest for similarly sized individuals and size had little effect on competition for food. The model predicted size divergence when size strongly affected competition for food. In the second model, we used a dynamic game to solve for optimal investment in growth suppression as a function of size structure. Investment in growth suppression was favoured only when dominants and subordinates were similar in size, generating size ratios different than those expected by chance. Variation in the feedbacks among growth, size and status can explain variation in emergent size structure of dominance hierarchies and its consequences for conflict within groups. This article is part of the theme issue ‘The centennial of the pecking order: current state and future prospects for the study of dominance hierarchies’.