] Perhaps I'm totally wrong about how common it was, or how
] expensive watches were.

No information on price, Lief but the link has a handy timeline on watch developements which indicates that several developments in the late 1700s made watches slimmer and more readily available. Eli Terry initiated mass production techniques in the US in the early 1800's but from what I can see it seems unlikely these developements would have influenced the price of watches even at the end of JA's time.