In this paper, we use weak measurement to study the mixed magneto-optical Kerr effects (MOKEs) in a magnetic single layer of Co and in organic/Co bilayer films. The relationship between the amplified shift and the MOKE parameters is theoretically established and then experimentally observed as a function of both the magnetization intensity and the magnetization direction in magnetic thin films with an arbitrary magnetization. Furthermore, we experimentally observe a magnetic coupling at the organic/ferromagnetic interface. Due to this being a robust coupling, there is a significant dependence of the amplified shift with the thickness of the organic layer. This work has value for its application in the magnetic measurement technique for the more general case based on weak measurement.