We explore the influence of effective mass (m*) on size-dependent linear and non-linear optical (NLO) response of one electron quantum dots in two dimensions with anharmonicity in the confinement potential. For some fixed values of transverse magnetic field strength (omega(c)), harmonic confinement potential (omega(o)), and anharmonic coupling strength (lambda), the interplay between the dot size (L) and dot effective mass (m*) in modulating the linear (alpha), the first (beta), and the second (gamma) NLO responses of the system is computed through a linear variational route. The investigation indicates a complicated interplay between the two controlling parameters. (C) 2008 Elsevier B.V. All rights reserved.