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Different properties of dark matter haloes, including growth rate, concentration, interaction history, and spin, correlate with environment in unique, scale-dependent ways. While these halo properties are not directly observable, galaxies will inherit their host haloes' correlations with environment. As a result, measures of environment have the potential to reveal how galaxy properties are correlated with halo properties beyond halo mass. We show results that different halo properties imprint distinct scale-dependent signatures in both the two-point correlation function and the distribution of distances to kth nearest neighbors. We show that these signatures are strong, and are accessible even with low-resolution (e.g., grism) spectroscopy at higher redshifts. Comparing observed two-point correlation functions for large and small galaxies at z=0, we use these results to show that neither classic galaxy size models (i.e., galaxy size being proportional to halo spin) nor more recent concentration-based models can be correct. Instead, we find that models where galaxy size is correlated with growth rate are better matches to observations. Finally, we discuss new machine learning methods to reveal halo properties for galaxy populations.