Transport signatures of exchange gap opening because of magnetic proximity effect (MPE) are reported for bilayer structures of Bi2Se3 thin films on yttrium iron garnet (YIG) and thulium iron garnet (TmIG) of perpendicular magnetic anisotropy (PMA). Pronounced negative magnetoresistance (MR) was detected, and attributed to an emergent weak localization (WL) effect superimposing on a weak antilocalization (WAL). Thickness-dependent study shows that the WL originates from the time-reversal-symmetry breaking of topological surface states by interfacial exchange coupling. The weight of WL declined when the interfacial magnetization was aligned toward the in-plane direction, which is understood as the effect of tuning the exchange gap size by varying the perpendicular magnetization component. Importantly, magnetotransport study revealed anomalous Hall effect (AHE) of square loops and anisotropic magnetoresistance (AMR) characteristic, typifying a ferromagnetic conductor in Bi2Se3/TmIG, and the presence of an interfacial ferromagnetism driven by MPE. Coexistence of MPE-induced ferromagnetism and the finite exchange gap provides an opportunity of realizing zero magnetic-field dissipation-less transport in topological insulator/ferromagnetic insulator heterostructures.