To become established upon zoonotic transfer, influenza A viruses (IAV) need to switch binding from "avian-type" α2-3-linked sialic acid receptors (2-3Sia) to "human-type" Siaα2-6-linked sialic acid receptors (2-6Sia). For the 1968 H3N2 pandemic virus, this was accomplished by two canonical amino acid substitutions in its hemagglutinin (HA) although a full specificity shift had not occurred. The receptor repertoire on epithelial cells is highly diverse and simultaneous interaction of a virus particle with a range of low- to very low-affinity receptors results in tight heteromultivalent binding. How this range of affinities determines binding selectivity and virus motility remains largely unknown as the analysis of low-affinity monovalent HA-receptor interactions is technically challenging. Here, a biolayer interferometry assay enabled a comprehensive analysis of receptor-binding kinetics evolution upon host-switching. Virus-binding kinetics of H3N2 virus isolates slowly evolved from 1968 to 1979 from mixed 2-3/2-6Sia specificity to high 2-6Sia specificity, surprisingly followed by a decline in selectivity after 1992. By using genetically tuned HEK293 cells, presenting either a simplified 2-3Sia- or 2-6Sia-specific receptor repertoire, receptor-specific binding was shown to correlate strongly with receptor-specific entry. In conclusion, the slow and continuous evolution of entry and receptor-binding specificity of seasonal H3N2 viruses contrasts with the paradigm that human IAVs need to rapidly acquire and maintain a high specificity for 2-6Sia. Analysis of the kinetic parameters of receptor binding provides a basis for understanding virus-binding specificity, motility, and HA/neuraminidase balance at the molecular level.