assimilated form of ad- "to, toward, before" before stems beginning in -t-; see ad-. In Old French and Middle English regularly reduced to a-, later restored.
late 14c., from Old English (Anglian) hlæhhan, earlier hliehhan, hlihhan "to laugh, laugh at; rejoice; deride," from Proto-Germanic *klakhjan (source also of Old Norse hlæja, Danish le, Old Frisian hlakkia, Old Saxon hlahhian, Middle Dutch and Dutch lachen, Old High German hlahhan, German lachen, Gothic hlahjan), from PIE *kleg-, of imitative origin (compare Latin cachinnare "to laugh aloud," Sanskrit kakhati "laughs," Old Church Slavonic chochotati "laugh," Lithuanian klagėti "to cackle," Greek kakhazein).
Originally with a "hard" -gh- sound, as in Scottish loch; the spelling remained after the pronunciation shifted to "-f."
If laugh were written as it is pronounced, laaff, there would be nothing in the word itself to put us in mind of the thing signified. The imitation begins to be felt in the guttural ach of G. lachen, and is clearly indicated in the reduplicate form of the Du. lachachen, to hawhaw or laugh loud, preserved by Kilian. [Hensleigh Wedgwood, introduction to "A Dictionary of English Etymology," 1878]
To laugh in one's sleeve is to laugh inwardly so as not to be observed:
If I coveted nowe to avenge the injuries that you have done me, I myght laughe in my slyve. [John Daus, "Sleidanes Commentaries," 1560]
"The phrase generally implies some degree of contempt, and is used rather of a state of feeling than of actual laughter" [Century Dictionary]. Related: Laughed; laugher; laughing.
Old English æt, from Proto-Germanic *at (source also of Old Norse, Gothic at, Old Frisian et, Old High German az), from PIE root *ad- "to, near, at." Lost in German and Dutch, which use their equivalent of to; in Scandinavian, however, to has been lost and at fills its place.
At is used to denote relations of so many kinds, and some of these so remote from its primary local sense, that a classification of its uses is very difficult. [OED]
In choosing between at church, in church, etc. at is properly distinguished from in or on by involving some practical connection; a worshipper is at church; a tourist is in the church. In 19c. it was used for points of the compass as regions of a country (at the South) where later tendency was to use in.
The colloquial use of at after where (as in where it's at) is noted in Bartlett (1859). At last is recorded from late 13c.; adverbial phrase at least was in use by 1775. At in Middle English was used freely with prepositions (as in at after, which is in Shakespeare), but this has faded with the exception of at about.
"baseball player's turn at the plate," 1912, originally a column heading in statistics tables, from the prepositional phrase.
"reception of visitors," 1745, noun use of prepositional phrase at home.
"in any way," mid-14c., originally used only affirmatively (as in I Samuel xx.6 in KJV: "If thy father at all misse me"); now it is overwhelmingly used only in the negative or in interrogatory expressions, formerly also in literary attempts at Irish dialect.