Novel phases of two dimensional electron systems resulting from new surface or interface modified electronic structures have generated significant interest in material science. We utilize photoemission spectroscopy to show that the near-surface electronic structure of a bulk insulating iridate Sr$_3$Ir$_2$O$_7$ lying near metal-Mott insulator transition exhibit weak metallicity signified by finite electronic spectral weight at the Fermi level. The surface electrons exhibit a unique spin structure resulting from an interplay of spin-orbit, Coulomb interaction and surface quantum magnetism, distinct from a topological insulator state. Our results suggest the experimental realization of a novel quasi two dimensional interacting electron surface ground state, opening the door for exotic quantum entanglement and transport phenomena in iridate-based oxide devices.