An enhancement of the spin-orbit effects arising on an interface between a ferromagnet (FM) and a heavy metal (HM) is possible through the strong breaking of the structural inversion symmetry in the layered films. Here, we show that an introduction of an ultrathin W interlayer between Co and Ru in Ru/Co/Ru films enables to preserve perpendicular magnetic anisotropy (PMA) and simultaneously induce a large interfacial Dzyaloshinskii-Moriya interaction (iDMI). The study of the spin-wave propagation in the Damon-Eshbach geometry by Brillouin light scattering spectroscopy reveals the drastic increase in the iDMI value with the increase in W thickness (tW). The maximum iDMI of -3.1 erg/cm2 is observed for tW = 0.24 nm, which is 10 times larger than for the quasi-symmetrical Ru/Co/Ru films. We demonstrate the evidence of the spontaneous field-driven nucleation of isolated skyrmions supported by micromagnetic simulations. Magnetic force microscopy measurements reveal the existence of sub-100-nm skyrmions in the zero magnetic field. The ability to simultaneously control the strength of PMA and iDMI in quasi-symmetrical HM/FM/HM trilayer systems through the interface engineered inversion asymmetry at the nanoscale excites new fundamental and practical interest in ultrathin ferromagnets, which are a potential host for stable magnetic skyrmions. © 2018 Author(s).