Pt/Co/heavy metal (HM) tri-layered structures with interfacial perpendicular magnetic anisotropy (PMA) are currently under intensive research for several emerging spintronic effects, such as spin-orbit torque, domain wall motion, and room temperature skyrmions. HM materials are used as capping layers to generate the structural asymmetry and enhance the interfacial effects. For instance, the Pt/Co/Ta structure attracts a lot of attention as it may exhibit large Dzyaloshinskii-Moriya interaction. However, the dependence of magnetic properties on different capping materials has not been systematically investigated. In this paper, we experimentally show the interfacial PMA and damping constant for Pt/Co/HM tri-layered structures through time-resolved magneto-optical Kerr effect measurements as well as magnetometry measurements, where the capping HM materials are W, Ta, and Pd. We found that the Co/HM interface play an important role on the magnetic properties. In particular, the magnetic multilayers with a W capping layer features the lowest effective damping value, which may be attributed to the different spin-orbit coupling and interfacial hybridization between Co and HM materials. Our findings allow a deep understanding of the Pt/Co/HM tri-layered structures. Such structures could lead to a better era of data storage and processing devices.