Kentucky windage is adjusting your side to side point of impact by guessing where you need your point of aim to be to achieve that point of impact without adjusting the sights. It could be to compensate for crosswinds on a long shot. Early precision marksmen used rifles instead of muskets, many of the early riflemen came from the hill country around Virginia, Tennessee, and Kentucky, as well as Pennsylvania. One of the more popular firs of rifle was the Kentucky Rifle which may have had a smaller bore and thus shot lighter bullets that could be more affected by the wind. Early sights didn't have a quick easy way to adjust side to side compensation or windage, some had some elevation adjustment, though most did not.
Put it all together and the origin is probably somewhere in there.
The Primitive sights on the early American Rifle AKA Kentucky rifle were not adjustable. The rifles were zeroed at maybe 50 yards. On targets beyond that the shooter had to know where the rifle "Threw" the ball and hold off right or left to compensate for distance. The rifle shot a patched round ball and would "Yaw" or drift according to the pitch of the rifling.
The hold over for drop was refereed to as Tennessee elevation. Humm? On that one your guess is as good as mine?
*grabs popcorn and prepares to be regailed yet again with origins of nautical terms*
Back in the days of wooden ships and iron men...
On the gun decks cannon balls were arranged in pyramid shaped stacks on s brass plate with indentations or holes cut in them to keep the foundation layer of cannon balls from rolling around as the ship would pitch in the sea. These plates were referred to as brass monkeys. Brass and iron being metals if differing densities would expand and contract at different rates as temperatures would change. Brass contracts considerably more and faster than iron. When temps got cold enough the holes or indentations would contract to a small enough diameter that they would force the still larger iron balls up and off the plate, sending them rolling around the gun deck. Thus the weather had gotten cold enough to freeze the balls off of a brass monkey.
Learned while touring the USS Constitution in Boston Harbor.