Understanding why food webs thrive or collapse is a major challenge that has been mostly studied in terms of consumer-resource interaction strengths or the topology of the interaction network. Yet the biological basis and relative importance of these properties are hotly debated. Here, we construct a model that incorporates body-mass constraints on key factors that influence food webs: the likelihood and strength of interactions, self-regulation, and total consumption rates. Our model predicts stability and connectance in real food webs ranging widely in species diversity (29-163 species) and trophic connectance (113-1086 interactions). Despite their absence in most research, we found that realistic self-regulation and consumption rate constraints are not only required to accurately predict stability but have stronger impacts than the more-frequently-studied interaction strengths. Our results demonstrate that food web stability is simultaneously impacted by multiple food web properties—all of which are naturally constrained by species masses.