Enhancement of magneto-optical effects in hybrid magneto-plasmonic systems has attracted considerable recent attention because of their potential for building non-reciprocal nanophotonic devices. Quantitative understanding of the fundamental origin and contributing mechanisms for the enhancement is crucial for optimizing applications. Here, we unravel different physical origins of the giant enhancement of Faraday rotation and ellipticity in a hybrid magneto-plasmonic system, namely, waveguided magneto-plasmonic crystal for excitation with transverse electric (TE) and transverse magnetic (TM) polarized light. With TE polarization excitation, where the surface plasmons are not directly excited, the natural weak value amplification of Faraday effects appearing due to the spectral domain interference of Fano resonance is the dominant cause of the enhancement. For TM polarization excitation, on the other hand, waveguide-plasmon strong coupling and its universal manifestation of avoided crossing plays an important role, leading to maximum enhancement of the magneto-optical effects in the avoided crossing regime.