  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. In this paper, we show how these characteristic environmental
signatures allow using measurements of galaxy environment to constrain which
dark matter halo properties are most tightly connected to observable galaxy
properties. We show that different halo properties beyond mass imprint distinct
scale-dependent signatures in both the galaxy two-point correlation function
and the distribution of distances to galaxies' $k$th nearest neighbours, with
features strong enough to be accessible even with low-resolution (e.g., grism)
spectroscopy at higher redshifts. As an application, we compute observed
two-point correlation functions for galaxies binned by half-mass radius at
$z=0$ from the Sloan Digital Sky Survey, showing that classic galaxy size
models (i.e., galaxy size being proportional to halo spin) as well as other
recent proposals show significant tensions with observational data. We show
that the agreement with observed clustering can be improved with a simple
empirical model in which galaxy size correlates with halo growth.
