We use KiDS weak lensing data to measure variations in mean halo mass as a function of several key galaxy properties (namely stellar colour, specific star formation rate, Sérsic index, and effective radius) for a volume-limited sample of GAMA galaxies in a narrow stellar mass range [M∗ ∼(2-5) × 1010 M⊙]. This mass range is particularly interesting, inasmuch as it is where bimodalities in galaxy properties are most pronounced, and near to the break in both the galaxy stellar mass function and the stellar-to-halo mass relation (SHMR). In this narrow mass range, we find that both size and Sérsic index are better predictors of halo mass than either colour or SSFR, with the data showing a slight preference for Sérsic index. In other words, we find that mean halo mass is more tightly correlated with galaxy structure than either past star formation history or current star formation rate. Our results lead to an approximate lower bound on the dispersion in halo masses among log M∗ ≈ 10.5 galaxies: We find that the dispersion is ≳ 0.3 dex. This would imply either that offsets from the mean SHMR are closely coupled to size/structure or that the dispersion in the SHMR is larger than what past results have suggested. Our results thus provide new empirical constraints on the relationship between stellar and halo mass assembly at this particularly interesting mass range.