I say it's a hand-made fishing weight. I live by coastal towns that date back to the 1800s. After storms on the beach, erosion reveals coins and targets from by-gone eras. Lead objects like that, start appearing when it gets down to barbers and seateds era. We reasoned they are fishing weights, because the have a hole in them.
Although today, people may buy ready-made fishing sinkers, back then people no doubt made their own. You say you found it next to a marsh, so maybe there was a body of water there, for fishing, at one time?