How does "drive out" shift to signify "weigh out"?
I boldened the relevant parts of the quotations, so that you don't have to read all of the quotations. I'm untrained at metaphors! How did "drive out" develop the metaphor of "weigh out"?
The adjective exact ‘precise’ and the verb exact ‘demand with severity’ have undergone considerable semantic divergence over the centuries, but they both go back to the same source, the Latin verb exigere (from which English also got essay, examine, exigent , and exiguous ). This, a compound of the prefix ex- ‘out’ and agere ‘lead, drive’ (source of English act and agent), meant originally ‘drive out’, but in due course it developed the metaphorical senses ‘demand’ (preserved in the English verb), ‘weigh accurately’, and ‘bring to completion or perfection’. These last two were taken up adjectivally in the Latin past participle exactus, from which English gets exact.
Like essay and exact, examine comes ultimately from Latin exigere, a compound verb formed from the prefix ex- ‘out’ and agere ‘lead, drive’ (source of English act and agent). This originally meant literally ‘drive out’, but a metaphorical sense ‘weigh accurately’ developed which was carried over into a derived noun exāmen ‘weighing’. This in turn formed the basis of another derivative, the verb exāmināre ‘weigh’, hence ‘weigh up, ponder, consider, test, examine’. The abbreviation exam for examination dates from the late 19th century.
Word Origins (2005 2e) by John Ayto. p 201 Right column.