this one is just a slightly unconventional usage of 'tight':

adv. (The adj. used adverbially.)

1. Soundly, roundly; = tightly 1. Now chiefly in colloq. phr. (good night) sleep tight, a conventional (rhyming) formula used when parting for the night or at bedtime. Also in slang phr. blow me tight: see blow

1933 E. O'Neill Ah, Wilderness! iii. ii. 101 Good night, Son. Sleep tight.