The influence of Re layer insertion either at the bottom or top interface of epitaxially grown Pt/Co/Pt heterostructures on their static and dynamic magnetic properties is discussed in terms of their crystalline structure. Magnetic properties were studied as a function of both Re and Co layer thicknesses (dRe and dCo, respectively) in the matrix-like samples with a double-wedge structure, in which the layer thickness gradients were oriented orthogonally. The comprehensive investigations of the changes in coercivity, perpendicular magnetic anisotropy, spin reorientation transition, interfacial Dzyaloshinskii-Moriya interaction (iDMI) and spin wave damping are reported. Two different magnetic phases depending on the Co layer thickness with volume anisotropies (determined without demagnetization term) of KV∼0.25 (low) and KV∼0.75 MJ/m3 (high) were observed. The relation between these phases depends on the stack sequence and thickness of Re inserted layer. For dRe = 0.2 ÷ 0.7 nm deposited as the bottom interface, dCo induced transition at dtr ∼ 2 nm from low to high volume anisotropy phases was observed. Low and high volume anisotropy phases are associated to Co fcc and hcp structural phases. The insertion of half atomic layer of Re had no influence on surface anisotropy but significantly enhanced iDMI above 1 pJ/m and reduced spin wave damping.