Etymology
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-et 
word-forming element, originally a diminutive suffix but not now always felt as one, Middle English, from Old French -et (fem. -ete; Modern French -et, -ette), from Vulgar Latin *-ittum/*-itta (source also of Spanish -eto/-eta, Italian -etto/-etta), of unknown origin. The French forms are reduced to -et in English, but later borrowings of French words in -ette tend to keep that ending.
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-let 
diminutive noun-forming element, Middle English, from Old French -elet, which often is a double-diminutive. It consists of Old French diminutive -et, -ette (see -et) added to nouns in -el, which in many cases represents Latin diminutive -ellus; see -el (2)). "The formation did not become common until the 18th c." [OED].
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-ette 
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."
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