The results of magnetic investigations of epitaxial trilayers Pt/Co/Pt asymmetrically modified by inserting W layer at the bottom or top Co interfaces in the wide ranges of Co and W layer thicknesses are reported. The samples were epitaxially grown on Pt buffer in double wedge geometry: the dCo thickness gradient of the continuous Co wedge was orthogonal to the dW thickness gradient of non-magnetic W underlayer (overlayer) deposited either as step-like or continuous wedge. Resulting samples have Pt/W/Co/Pt (Pt/Co/W/Pt) stacking sequences. The influence of (dCo, dW) on static magnetization reversal processes were studied using magnetooptical Kerr effect; Brillouin light scattering (BLS) method was applied for dynamical characterization. The magnetic dead layer thickness d0 abruptly increases until dW reaches ∼ 0.5 nm for both orderings. Then its value saturates for Pt/Co/W/Pt, while for Pt/W/Co/Pt samples a slow growth is observed. For dCo corresponding to out-of-plane magnetization the inserting of W layer leads to the strong reduction in coercivity (two orders of magnitude) and transition to in-plane magnetization in the case of Pt/W/Co/Pt ordering, while the Pt/Co/W/Pt samples demonstrates weak changes of coercivity with small change in magnetic anisotropy. The strength of interfacial Dzyaloshinskii-Moriya interaction (iDMI) and spin wave damping for selected dCo thicknesses as a function of dW were derived from BLS measurements. Inserting W with thickness dW ∼ 0.1 nm induces significant iDMI changes, iDMI saturates for dW > 0.4 nm. Our findings demonstrate the efficiency of thin W interlayer on modification of magnetic parameters in Pt/Co/Pt trilayer.