Etymology of informal use of “favor” in the U.S

I know in some U.S. dialects, “favor” as a verb is used informally to indicate that two people share a similar physical appearance, especially when the two look so similar that one's physical appearance makes you think of the other. So I guess you could use it in place of “looks like,” or “reminds me of”.

Eg: That child favors her father. I don’t see how you could possibly think she favors her mother.

Does anyone know the etymology of this particular use of “favor”?

As commenters have indicated, this use of favor has a long history. It is indeed Middle English (favour) with a French parallel (faveur) - all according to the OED.

The transitive verb meaning

to resemble in face or features; rarely, to resemble generally have the look of...

can be traced to Ben Jonson in 1609, and a parade of others running into the 19th century (thanks and a hat-tip to @RaceYouAnytime).

A possibly earlier noun usage

appearance, aspect, look

is cited as early as 1450 by the OED. Whether or not this relates to "favour" as a ribbon or badge to be worn in competition, it seems to cement this "representative" idea of favor/favour firmly in the history of the language. Interestingly, these definitions are labeled "archaic" or "dialect" by OED. Like many popular expressions, this one must have migrated to the American colonies, where it became entrenched or isolated depending on regional populations.

The rest lies somewhere between history and mystery.