Rare earth (RE)–transition metal (TM) ferrimagnetic thin films have attracted significant interest for their broad range of functionalities associated with the reduced net magnetization. Here, we study the magnetic properties of Tb-based RE–TM ferrimagnetic [Tbx(FeCo)1−x] thin films. We find that the Tb concentration at which the magnetic moments of the RE- and TM- sublattices compensate increases with decreasing film thickness when the films are grown on Pt underlayers. For the thinnest TbFeCo films (1.5 nm-thick), the magnetic compensation is not observed at room temperature, suggesting that the Tb atoms do not contribute to the magnetization. In these thin films, the perpendicular magnetic anisotropy (PMA) increases when a thin Co layer is inserted, while it drops to zero when a thin Tb layer is inserted. Such contrasting behavior reveals that the PMA originates from the Pt/Co interface. The Tb concentration at which magnetic compensation occurs decreases when the underlayer is changed from Pt to Ta. We infer that Tb becomes magnetically inactive due to intermixing with the Pt underlayer, causing the reduction in PMA.