late 13c., from Old French cote "hut, cottage" + Anglo-French suffix -age (probably denoting "the entire property attached to a cote"). Old French cot is probably from Old Norse kot "hut," cognate of Old English cot, cote "cottage, hut," from Proto-Germanic *kutan (cf. Middle Dutch cot, Dutch kot).
Meaning "small country residence" (without suggestion of poverty or tenancy) is from 1765. Modern French cottage is a 19c. reborrowing from English. Cottage industry is attested from 1921. Cottage cheese is attested from 1831, American English, earliest in reference to Philadelphia: