What does an overnight chill do to cookie dough, that a 4 hour chill doesn't?

The rest period hydrates the starches in flour, giving the dough a firmer and more workable texture (there is some very minor gluten development, but its mostly the expansion of the starch bundles with water). In many cookies, the flavors will also mature and improve, especially with cocoa in the recipe.

In many recipes, the cooling from refrigeration is itself part of the point--doughs may be easier to roll and cut when they are cool due to chilling of the fat. Most dietary fats are waxy, which means they don't have a single set freezing/melting point, but rather get more viscous or eventually firmer then hard as temperature drops.

For example, linzer cookie dough is very frangible, and the chilling and hydration make rolling and cutting much easier.

Generally, most of this affect is going to happen in the first 8 hours or so. The overnight thing is simply for convenience in most cases. In fact, 4 hours is often enough, although obviously not in your case.

If the major effect is chilling in your recipe, by flattening the dough to a disk, or lengthening it to a log (thus increasing surface area) compared to a ball, it will chill more rapidly. You mentioned this is a high fat recipe--if that fat is butter (as it so often is with cookies), that may help.

Generally - overnight chilling just ensures that you actually DO chill for 4 hours. However - in your case the fat needed to penetrate the flour and harden up. It's a slow process (deopending on the type of fat), but well worth the wait.

For example - olive oil hardens up in the fridge, but not in 4 hours, even though it reaches the right temperature. The structure has to change. Think about honey. It hardens up, but over a long period of time.

I do not know the chemistry involved, but longer dough refrigeration toughens the dough, and makes it more cohesive. It, like any refrigeration, also changes the texture of the finished product (usually making it chewier).