Spin-orbit torques (SOTs) have opened a new path to switch the magnetization in perpendicularly magnetized films and are of great interest due to their potential applications in novel data storage technology, such as the magnetic random access memory (MRAM). The effective manipulation of SOT has thus become an important step towards these applications. Here, current induced spin-orbit effective fields and magnetization switching are investigated in Pt/Ta/CoFeB/MgO structures with bilayer heavy metals. With a fixed thickness (1 nm) of the Ta layer, the magnitude and sign of current induced spin-orbit effective fields can be continuously tuned by changing the Pt layer thickness, consistent with the current induced magnetization switching data. The ratio of longitudinal to transverse spin-orbit effective fields is found to be determined by the Ta/CoFeB interface and can be continuously tuned by changing the Pt layer thickness. The Dzyaloshinskii-Moriya interaction (DMI) is found to be weak and shows an insignificant variation with the Pt thickness. The results demonstrate an effective method to tune SOTs utilizing bilayer heavy metals without affecting the DMI, a desirable feature which will be useful for the design of SOT-based devices.