Thanks for the question.  I have search on internet by typing this word BEEG. But Could not find the actual meaning of this question.
According to Wikipedia, Beeg may refer to:
Beeg, Netherlands, – the Limburgish name of Grevenbicht, a village in the Netherlands
Bluegrass Beeg, – a music festival taking place in Beeg
Gunda Beeg, – 19th-century German writer and activist
Beeg Boy – nickname for Rico Carty (born 1939), baseball player.

And according to urban dictionary,
Beeg is Another word of “Blow Job” When a man gets his penis sucked.
Example: Tyler’s dad offered him a beeg.
by Taavi KH February 16, 2009