acronym for sealed with a kiss, attested from 1911, in a legal publication quoting a letter from 1909:
"... Well Kid I don't know nothing else to say only that I hope to see your sweet face Sat. Good by from your Dear Husban to his sweet little wife. P. S. excuse bad writing and mispelled words take all mistakes as kisses. S.W.A.K. * * *" This letter was postmarked at Des Moines October 20, 1909, addressed to Carrie Sprague at Jefferson, Iowa, and reached the latter place October 21, 1909. [State v. Manning (a conspiracy-to-lure-women-to-prostitution case), Supreme Court of Iowa, Nov. 16, 1910, reported in Northwestern Reporter, vol. cxxviii, 1911]
Popularized in soldiers' letters home in World War I. It probably is meant also to echo the sound of a kiss. Compare Middle English swack "a hard blow" (late 14c.).