Weakly coupled molecular junctions are quite active and important field of research as they exhibit various non-linear transport phenomena. We have investigated the carrier transport through weakly coupled B 2 C 2 N 2 H 6 molecules using quantum many body approach coupled with kinetic (master) equations. Various types of non-linear current voltage characteristics, such as, negative differential conductance (NDC), rectifications, Coulomb staircase, which are hallmark of multistate transport devices, have been obtained. Source-drain voltage induces changes in the occupation probabilities of low-lying many body states depending on the nature of the carrier transport.The nature of the carrier transport directly controls the net current flowing through the molecular junctions. We further investigated the effect of different kinds of perturbations such as application of gate voltage and magnetic field perpendicular to the direction of the molecule upon the carrierflow through various molecular bridges. Interestingly, we find that depending on the strength of the applied perturbing field, several phenomena, such as, switching off of the current, suppression of NDC etc. appears in the device. Fundamentally, this applied perturbation modifies both the site charge density as well as occupation probabilities of transport active channels, resulting in significant alteration in the transport behavior of the molecular junction.