Surprising weak assembly behavior has lately been found in binary aqueous solvents containing antagonistic salt. The underlying mechanism is still under debate, particularly the role of ion size asymmetry. Here we use small-angle X-ray scattering to study the effect of ion size asymmetry on the mesoscale ordering in a binary solvent composed of water and 2,6-dimethylpyridine with added symmetrical quaternary ammonium salt. By systematically elongating the hydrocarbon side-chain lengths, and hence developing cation-to-anion size asymmetry, we provide the first experimental evidence of a gradual build-up of the solvent's mesoscale ordering. These results are in qualitative agreement with model-independent theoretical predictions.