Learn English – What does “keeping someone in shoe leather” means

The phrase is "shoe leather reporting".

I believe the meaning here is that genuine reporters will be out on the street walking, investigating, talking first-hand i.e. wearing out the leather of their shoes for a good quote or story. This is as opposed to new media where people pick up online research or data and pass it off as journalism.

My assumption turned out right, I've updated to include a reference

Part of the problem is that journalism terminology glorifies "shoe-leather reporting," whereby you pound the pavement so often you wear out the soles of your shoes.

"Heavy" in "heavy black coats" is a reference to the thickness of the fabric. It is not, for instance, a light windbreaker, it's made of a relatively sturdy fabric. There is not generally a "heavy black" color, though one might see it in literary contexts.

The "light" in "light gray jacket," however, I would usually take to mean a jacket of unspecified weight in a light-gray color, unless context clearly indicated "light" was a fabric weight.