Portion comes from Latin portiō ('a share'), related to pars ('a part'). Originally it meant your allotted share of life — your destiny. The food-serving sense is the same concept on a smaller scale.
A part of something divided between people; an amount of food served to one person; a person's destiny or lot in life.
From Old French porcion, from Latin portiōnem (nominative portiō) meaning 'a share, a part', related to pars (genitive partis) meaning 'a part, a piece, a share'. Both derive from Proto-Indo-European *per- meaning 'to grant, to allot'. The word carried a sense of destiny from early on: your portion was not just food on a plate but your allotted share of life. This fatalistic sense
In medieval English, your portion was your destiny — the share of fortune allotted to you by God. A dowry was called a marriage portion: the share a bride brought to her new household. The phrase 'the Lord is my portion' appears throughout the Psalms. The modern restaurant meaning — a portion of chips — is the same ancient idea