Old English forca "forked instrument used by torturers," a Germanic borrowing (cf. Old Norse forkr) from Latin furca "pitchfork; fork used in cooking," of uncertain origin.
Table forks were not generally used in England until 15c. The word is first attested in this sense in English in a will of 1463, probably from Old North French forque (Old French furche, Modern French fourche), from the Latin word. Of rivers, from 1753; of roads, from 1839.
"to divide in branches, go separate ways" (early 14c.), from fork (n.). Related: Forked; forking. The slang verb phrase fork up (or out) "give over" is from 1831.
To pay; give; contribute: Fork up the cash/ I imagine he used a picture to make you fork over the dough (first form 1835+)