Armchair graphene nanoribbons (AGNRs) may present intrinsic semiconducting bandgaps, being of potential interest in developing new organic-based optoelectronic devices. The induction of a bandgap in AGNRs results from quantum confinement effects, which reduce charge mobility. In this sense, quasiparticles' effective mass becomes relevant for the understanding of charge transport in these systems. In the present work, we theoretically investigate the drift of different quasiparticle species in AGNRs employing a 2D generalization of the Su-Schrieffer-Heeger Hamiltonian. Remarkably, our findings reveal that the effective mass strongly depends on the nanoribbon width and its value can reach 60 times the mass of one electron for narrow lattices. Such underlying property for quasiparticles, within the framework of gap tuning engineering in AGNRs, impact the design of their electronic devices.