  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, Sersic index, and effective radius) for a volume-limited
sample of GAMA galaxies in a narrow stellar mass range ($M_* \sim 2$--$5 \times
10^{10}$ Msol). 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 Sersic
index are better predictors of halo mass than either colour or SSFR, with the
data showing a slight preference for Sersic 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 $\log M_*
\approx {10.5}$ galaxies: we find that the dispersion is $\gtrsim 0.3$ 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 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.
