The story
1585, due to association with waterfowl. The precise origin is unclear, and may be from ducks taking off from a pond, or making rings when splashing, or bobbing their heads. Early references are primarily to “making” ducks and drakes, suggesting that the circular rings produced by the skipping stone resemble those created by splashing waterfowl. Sense “to squander, to throw away” shortly thereafter, attested 1614, from sense of “throwing money away, as if throwing stones away in this pastime”.
Etymology from Wiktionary, CC BY-SA 4.0.