We study the evolution of non-linear structure as a function of scale in samples from the 2dF Galaxy Redshift Survey, constituting over 221000 galaxies at a median redshift of z = 0.11. The two flux-limited galaxy samples, located near the Southern Galactic Pole and the Galactic equator, are smoothed with Gaussian filters of width ranging from 5 to 8h-1Mpc to produce a continuous galaxy density field. The topological genus statistic is used to measure the relative abundance of overdense clusters to void regions at each scale; these results are compared with the predictions of the analytic theory, in the form of the genus statistic for (i) the linear regime case of a Gaussian random field and (ii) a first-order perturbative expansion of the weakly non-linear evolved field. The measurements demonstrate a statistically significant detection of an asymmetry in the genus statistic between regions corresponding to low- and high-density volumes of the Universe. We attribute the asymmetry to the non-linear effects of the gravitational evolution and biased galaxy formation, and demonstrate that these effects evolve as a function of scale. We find that neither analytic prescription satisfactorily reproduces the measurements, though the weakly non-linear theory yields substantially better results at some scales, and we discuss the potential explanations for this result.