Origins
A portion of food and a portion of destiny are the same word used at different scales. The English word comes from Old French porcion, from Latin portiō — 'a share, a part' — related to pars ('a part, a piece'). The deeper root is Proto-Indo-European *per-, meaning 'to grant, to allot'.
The fatalistic sense came first in English. In medieval usage, your portion was the share allotted to you — by birth, by God, by fortune. The Bible uses the word this way throughout: 'The Lord is my portion' (Psalms 119:57). A dowry was a marriage portion — the material share a woman brought to her husband's household.
The food sense developed naturally from the idea of dividing and allotting. When a household divided a meal, each person received their portion. The word carries the same distributive logic whether applied to a life or a plate of food.
Latin Roots
Latin pars generated one of the largest word families in English. Part is the most direct descendant. Proportion is how parts relate to each other. Participate is to take part. Partner was originally 'parcener' — someone who shares a portion. Party began as a 'part' or side in a dispute before becoming a social gathering. Apportion is to distribute portions formally.
The restaurant use — 'portion control', 'generous portions' — arrived in the 20th century, but the underlying idea is thousands of years old: how much is your share?