From baqa'; a section (half) of a shekel, i.e. A beka (a weight and a coin) -- bekah, half a shekel.
see HEBREW baqa'
H1235. beqa
בֶּ֫קַע noun [masculine] fraction, half, i.e. half-shekel, a weight; מִשְׁקָלוֺ בֶּקַע Genesis 24:22, compare Hesychius in LagGes. Abh 199, 1. 18 βακαίον [Lag βέκαον] μέρον τι; see also בֶּקַע Exodus 38:26 (= הַשֶּׁקֶל מַחֲצִית).