gravy n.

late 14c. (perhaps mid-13c. in Anglo-French), grave, gravei, gravi, greve, gravey, gravee, grovi, grauvey, with u/v variation typical of medieval spelling. From Old French gravé, graué, "seasoned broth or sauce," ultimately from Persian zirbaja, said by H.F. Amedroz to mean “concoction in a pot.” The unattested intermediate term should have been something like *girveie (see evolution of ginger for comparison.) 

The dish became popular in Europe in the 14th century, probably introduced through the Emirate of Granada in what is now Spain.

Recipe for Zîrbâja […] Take a young, cleaned hen and put it in a pot with a little salt, pepper, coriander, cinnamon, saffron and sufficient of vinegar and fresh oil, and when the meat is cooked, take peeled, crushed almonds and good white sugar, four ûqiyas of each; dissolve them in rosewater, pour in the pot and let it boil; then leave it on the embers until the fat rises. It is the most nutritious of dishes and good for all temperaments; this dish is made with hens or pigeons or doves, or with the meat of a young lamb. [An Anonymous Andalusian Cookbook of the 13th Century, translated by Charles Perry.]

Conyngys in graueye. Take Conyngys, and make hem clene, and hakke hem in gobettys, and sethe hem, other larde hem and Rost hem; and thanne hakke hem, and take Almaundys, and grynde hem, and temper hem vppe with gode Freysshe brothe of Flesshe, and coloure it wyth Safroun, and do ther-to a porcyon of flowre of Rys, and do ther-to then pouder Gyngere, Galyngale, Canel, Sugre, Clowys, Maces, and boyle it onys and sethe it; then take the Conyngys, and putte ther-on, and dresse it and serue it forth. [Harleian MS 279, date ca. 1420]

It is usually said that gravé is a non-word created as a mistranscription of grané, a similar mixture with which it is indeed conflated in French manuscripts. Grané is usually supposed to be from Medieval Latin granatum “corned, grained” but this is unattested in the context of this sauce. It is as likely in this case to be from "Granada" (see Granada.) 

There may have been a second word, combined through folk-etymology, that led to the secondary sense of "juice of cooked meat." Perhaps Old French engravee "carved, sliced" or Old English greofa, an oil-pan (related to greaves, 1610s, "fibrous matter cooked out of animal fat.")

In Middle English the word grave is glossed against Latin garus, "a type of fish used for making sauce" and promulada, probably from promulsis, an old appetizer of eggs and fish. The sense of broths or drippings appears to originally be of fishes, then soon extended to meat drippings or gelatin, which sense grows dominant in English from mid-15c, though still used most typically of fish or other seafood till 16c.

As "a sauce made with meat drippings," 1670s, originally sauce gravy or gravy sauce. Applied to vegetarian mixtures by 1875. The meaning "tomato sauce" (chiefly Italian-American) is by 1978, evidently from certain Italian dialects differentiating tomato puree (salsa, "sauce") from the cooked tomato sauce (sugo, translated "gravy" in many 19c. and 20c. Italian-English dictionaries, or ragu, etc.)

The meaning "money easily acquired" is attested by 1910; gravy train (by 1899) as something lucrative or productive is said to have been originally railroad slang for a short haul that paid well. Gravy-boat "small, deep dish for holding gravy or sauce" is from 1827.