wee 1 
(wē)
(wē)adj. we·er, we·est
Very small; tiny. See Synonyms at small.
n.
Scots
Idiom: Scots
A short time; a little bit.
wee hours
The early hours of the morning right after midnight: "post-disco electronic rhythms that propel clubgoers into the wee hours" (Jon Pareles).
[Middle English wei, we, a small amount, small, from Old English wǣge, wēg, weight; see wegh- in the Appendix of Indo-European roots.]