The Dzyaloshinskii-Moriya interaction (DMI) manifesting in asymmetric layered ferromagnetic films gives rise to non-colinear spin structures stabilizing magnetization configurations with nontrivial topology. In this work magnetization reversal, magnetic domain alignment, and strength of DMI are related to the crystalline structure of W/Co/Pt multilayers grown by molecular beam epitaxy. The applied growth method enables the fabrication of layered systems with higher crystalline quality than commonly applied sputtering techniques. A relatively high value of the D coefficient was determined from the aligned magnetic domain stripe structure, substantially exceeding 2 mJ m-2. The highest value of DMI strength Deff = 2.64 mJ m-2 and surface DMI parameter DS = 1.83 pJ m-1 have been observed for a repetition number equal to 10. The experimental results correlate exactly with those obtained from the micromagnetic modelling and density functional theory calculations performed for the well-defined layered stacks. This high value of DMI strength originates from the additive contributions of the interfacial atomic Co layers at the two types of interfaces.