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Organismal traits and their evolution can strongly influence food web structure and dynamics. To what extent the evolution of such traits impacts food web structure, however, is poorly understood. Here, we investigate a simple three-species omnivory food web module where the attack rates of all predators evolve as ecological dynamics unfold, such that predator trophic levels are themselves dynamic. We assume a timescale where other vital rates that govern population dynamics are constant and incorporate a well-known tradeoff between attack rates and the conversion of prey into predator biomass. We show that this eco-evolutionary model yields a surprisingly rich array of dynamics. Moreover, even small amounts of selection lead to important differences in the abundance, trophic, and biomass structure of the food web. Systems in which intermediate predators are strongly constrained by tradeoffs lead to hourglass-shaped food webs, where basal resources and top predators have large abundances, but intermediate predators are rare, like those observed in some marine ecosystems. Such food webs are also characterized by a relatively low maximum trophic level. Systems in which intermediate predators have weaker tradeoffs lead to pyramid-shaped food webs, where basal resources are more abundant than intermediate and top predators, such as those observed in some terrestrial system. These food webs also supported a relatively higher maximum trophic level. Overall, our results suggest that eco-evolutionary dynamics can strongly influence the abundance-, trophic-, and biomass-structure of food webs, even in the presence of small levels of selection, thus stressing the importance of taking traits and trait evolution into account to further understand community-level patterns and processes.