Warming and eutrophication are two of the most important global change stressors for natural ecosystems, but their interaction is poorly understood. We used a dynamic model of complex, size‐structured food webs to assess interactive effects on diversity and network structure. We found antagonistic impacts: Warming increases diversity in eutrophic systems and decreases it in oligotrophic systems. These effects interact with the community size structure: Communities of similarly sized species such as parasitoid–host systems are stabilized by warming and destabilized by eutrophication, whereas the diversity of size‐structured predator–prey networks decreases strongly with warming, but decreases only weakly with eutrophication. Nonrandom extinction risks for generalists and specialists lead to higher connectance in networks without size structure and lower connectance in size‐structured communities. Overall, our results unravel interactive impacts of warming and eutrophication and suggest that size structure may serve as an important proxy for predicting the community sensitivity to these global change stressors.