Under the old Chinese weight system, one
斤 (catty) was 16
两 (tael) - so 'half a catty' equaled 'eight taels' exactly. The phrase appears in the Song-dynasty Chan Buddhist text
《五灯会元》 (Compendium of the Five Lamps):
秤头半斤,
秤尾八两 - 'one end of the scale half a catty, the other end eight taels.' Modern China shifted to a 10-tael
斤 in 1959, but the idiom kept the older math.