Reeves' Wrecking Ball Will Be Swinging...
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For more on marking an answer as the "Best Answer", please visit our FAQ.To see what the noted lexicographer and etymologist, Michael Quinion, has to say on the subject, click http://www.worldwidewords.org/qa/qa-sle1.htm I'm always happy to go with what he says.
According to Oxford, the adverb "tightly" used to mean "soundly, properly, well, effectively." So "sleep tight" means "sleep well;" it has nothing to do with bed ropes. See the following URL:
http://www.askoxford.com/asktheexperts/faq/aboutwordorig ins/tight?view=uk