Recent advances in microscopy, such as confocal scanning laser techniques, now permit the direct positional tracking of large numbers of colloidal particles, both in the bulk and near interfaces. We are approaching a point where the microscopically measured density profiles of colloidal sediments may be quantitatively compared with modeling results from theory and simulation. In this paper we compare the sedimentation profiles from confocal scanning laser microscopy experiments with those predicted by a closure-based classical density functional theory (DFT), for 700-nm fluorescent-core silica particles under normal gravity. We emphasize that the nonlocal DFT used here is capable of predicting the structure of the sediment at length scales comparable to the colloidal particle size. Excellent quantitative agreement was observed for the systems with lower, fluid-like colloid volume fractions (shallow sediments), but agreement grew worse as interfacial layering intensified and was quite poor when crystalline phases formed. We also applied DFT in an inverse sense, using the measured colloid density profile to extract the underlying colloid-surface potential; this can be thought of as a microscopic analogue to the well-known procedure of using the macroscopic (coarse-grained) density profile to extract the osmotic equation of state. For the shallow sediments, the inverse DFT calculations reproduced the true colloid-surface potential to within 0.2 kT at all elevations. This result indicates promise in using colloidal ensembles to rapidly map O(kT) surface energetics in a variety of nano- and bio-technology applications.