Current-perpendicular-to-the-plane giant magnetoresistance (CPP-GMR) read sensors based on Heusler alloys are promising candidates for ultrahigh areal densities of magnetic data storage technology. In particular, the thickness of reader structures is one of the key factors for the development of practical CPP-GMR sensors. In this research, we studied the dependence of the free layer thickness on the stability of the Co2(Mn0.6Fe0.4)Ge Heusler-based CPP-GMR read head for an areal density of 1 Tb/in2, aiming to determine the appropriate layer thickness. The evaluations were done through simulations based on micromagnetic modelling. The reader stability indicators, including the magnetoresistance (MR) ratio, readback signal, dibit response asymmetry parameter, and power spectral density profile, were characterized and discussed. Our analysis demonstrates that the reader with a free layer thickness of 3 nm indicates the best stability performance for this particular head. A reasonably large MR ratio of 26% was obtained by the reader having this suitable layer thickness. The findings can be utilized to improve the design of the CPP-GMR reader for use in ultrahigh magnetic recording densities.