origin of: sleep tight, make sure the bugs don’t bite

Solution 1:

It begins with the rhyme that good parents (from at least the 50's) tell their children as they tuck them into bed and immobility.; Good night, Sleep tight, Don't let the bedbugs bite.

Like any good rhymes the origin is in dispute.

This source is so good I've included a bit below. it is here: https://www.bedbugguide.com/dont-let-bed-bugs-bite-origin-rhyme/

Some historians refute these theories [above] and point to the Oxford English Dictionary, which claims ‘sleep tight’ simply means to ‘sleep soundly’.

Etymologist [bug scientist] Barry Popik claims the rhyme actually originated in the USA in the 1860s, and in some versions the biting referred to mosquitoes. One version from the 1860s is ‘Good night, sleep tight, wake up bright in the morning light, to do what’s right, with all your might.’

In a novel called ‘Boscobel’ written in 1881 by Emma Mersereau Newton, a boy says to his parents, ‘Good night, sleep tight; And don’t let the buggers bite.’ And in the 1884 book ‘Boating Trips’ by Henry Parker Fellows, a little girl says ‘Good-night. May you sleep tight, where the bugs don’t bite!’.

The precise phrase ‘Good-night, Sleep tight, Don’t let the bedbugs bite’ first appears in the 1896 book ‘What They Say in New England: A Book of Signs, Sayings, and Superstitions’, and it later appeared in a 1923 text by F. Scott Fitzgerald.