I list the references that I found so far. Shortly, the first appearance of the term was in 1670, first appearance in in close meaning was in 1827, first appearance in a biological paper was in 1923 and first appearance in statistics was in 1935. However, the references indicate that there are gaps in this chronology.
Earliest reference I found was The flying pen-man; or, The art of short-writing by William Hopkins (teacher of stenography.) in 1670. However, it is a table of words with "overfit" as one of them and the context or meaning is not clear.
I check the other references before 1800 and those were transcription errors, "over, fit" or "overfet".
The earliest appearance in context I found was in "The Enigmatical Entertainer and Mathematical Associate ..., Issue 1" in 1827 saying: "I , though for poetry not overfit , 7 Will boldly dare to lay down rules for wit ;" hence the meaning of overfit here is "fit too well" but in a positive meaning.
It seems that Darwin's "On the Origin of Species" in 1859 made the concept of fitting popular.
Bray, Charles I. "Fitting livestock for show." Bulletin (Colorado Agricultural College. Extension Service); 171A (1923). : "They believe that these are almost equally valuable, and that there is less danger of over-fitting the pigs than with whole milk."
The 1934 paper Twenty-Two Years of the Eastern Percheron Futurity mentions the penalty of over-fitting yet regarding stallions.
The Quarterly Review of Biology Sep 1935 Volume 10, Number 3pp. 341 – 377, saying : "Perhaps we are old fashioned but to us a six-variate analysis based on thirteen observations seems rather like overfitting". So it was well known and maybe a bit old-fashioned during 1935 already.
First statistics reference to over fitting I found appears in "Tests of Fit in Time Series", 1952. Yet it says: " Such a graduation implies a gross overfitting, but this can be allowed for." Using overfitting as a well known concept.
It is possible that the reference is The Quarterly Review of Biology Sep 1935 Volume 10, Number 3pp. 341 – 377, yet I couldn't verify it.
I'll be happy to learn that sheep are the origin of a central concept in AI but I'd like to see references. Reference not related to sheep are welcome too.