Spreading populations are subject to evolutionary processes acting on dispersal and reproduction that can increase invasion speed and variability. It is typically assumed that dispersal and demography traits evolve independently, but abundant evidence points to correlations between them that may be positive or negative, genetic or environmental. We sought to understand how demography-dispersal correlations modify the eco-evolutionary dynamics of range expansion. We first explored this question with the beetle Callosobruchus maculatus, a laboratory model in which evolutionary acceleration of invasion has been demonstrated. We then built a simulation model to explore the role of trait correlations in this system and more generally. We found that positive correlations amplify the positive influence of evolution on speed and variability, while negative correlations (such as we found empirically) constrain that influence. Strong negative genetic correlations can even cause evolution to decelerate invasion. Heritable and environmental correlations had similar effects on some measures of invasion but different effects on others. Model results enabled us to retrospectively explain invasion dynamics and trait evolution in C. maculatus, and may similarly aid the interpretation of other field and laboratory studies. Non-independence of demography and dispersal is an important consideration for understanding and predicting outcomes of range expansion.