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1.
The accidental merging of the words 'Wee' and 'Beer' When you are a tad intoxicated, and need both Urgently,
pissed guy: " guys......... i need a . . . . . . Weer
by COCKYGON June 28, 2012
 
2.
Literally, more wee. Something smaller than normal (especially if typically small) in a cute, quaint, or Scottish/Irish/Hobbit sort of way.

Pronunciation: Wee-er
"Wow! She's even weer than I remember!"

or
"That Frodo Baggins is weer than you'd expect!"
by Jason Jaques-Pierre March 03, 2010