A number of years ago, Robert F. Smith compared the Nephite weights and measures with Horus-eye fractions from Egypt. One need not go into the advantages and disadvantages of such a proposal to note that another possibility presents itself.
To review, the Book of Mormon lays out the following values (Alma 11:4-19):
2 leahs = 1 shiblum
2 shiblums = 1 shiblon
2 shiblons = senum
2 senums = 1 amnor
2 amnors = a ezrom
At least as early as the third to fifth century BC, Southern Arabia had a system of values that also doubled in size.
2 kyš = 1 šśʿ
2 šśʿ = 1 tmrt
2 ʾtmr = 1 gms
2 ʾgms = 1 nṣf
2 ʾnṣf = 1 K
2 K = 1 ʾrbʿt
We also have an idea of some prices from the time. A herd animal normally cost between 1 ʾrbʿt and 1 tmrt and 1 ʾrbʿt, 1 gm, and 1 tmrt.
(See Peter Stein, Die altsüdarabischen Minuskelinschriften auf Holzstäbschen aus der Bayerischen Staatsbibliothek in München (Tübingen: Ernst Wasmuth, 2010), 1:79-85.)
While we do not know the precise origin of the Nephite system, the South Arabian parallel may provide another possibility.