the adverb in attached to a verb as a word-forming element, by 1960, abstracted from sit-in, which is attested from 1941 in reference to protests and 1937 in reference to labor union actions (which probably was influenced by sit-down strike) but was popularized in reference to civil disobedience protests aimed at segregated lunch counters.
As a word-forming element it was extended first of other types of protests, then by 1965 to any sort of communal gathering (such as love-in, attested by 1967). In labor actions it was perhaps less useful: "a mass of workers calling in sick to absent themselves in protest" was called both a sick-out (1970) and a sick-in (1974).
diminutive word-forming element, from Old French -ette (fem.), used indiscriminately in Old French with masculine form -et (see -et). As a general rule, older words borrowed from French have -et in English, while ones taken in since 17c. have -ette. In use with native words since late 19c., especially among persons who coin new product names, who tend to give it a sense of "imitation, a sort of" (for example flannelette "imitation flannel of cotton," 1876; leatherette, 1855; linenette, 1894). Also in such words as lecturette (1867), sermonette, which, OED remarks, "can scarcely be said to be in good use, though often met with in newspapers."