The phase diagram of Sr3Ru2O7 shows hallmarks of strong electron correlations despite the modest Coulomb interaction in the Ru 4d shell. We use angle-resolved photoelectron spectroscopy measurements to provide microscopic insight into the formation of the strongly renormalized heavy d-electron liquid that controls the physics of Sr3Ru2O7. Our data reveal itinerant Ru 4d-states confined over large parts of the Brillouin zone to an energy range of <6 meV, nearly three orders of magnitude lower than the bare band width. We show that this energy scale agrees quantitatively with a characteristic thermodynamic energy scale associated with quantum criticality and illustrate how it arises from a combination of back-folding due to a structural distortion and the hybridization of light and strongly renormalized, heavy quasiparticle bands. The resulting heavy Fermi liquid has a marked k-dependence of the renormalization which we relate to orbital mixing along individual Fermi surface sheets.