A slang term, usually found in the west of scotland although is possible all over. A shortening of the term "deep trouble" or "deep shit" or other negative connotation.
Went out of fashion earlier this century although can still be found in use today, particularly amongst younger kids.

An adjective used to describe the feeling when contemplating or discussing a deep topic such as the meaning of life or the existence of god

is a gay (or 'ghey' as she like to put it)

Saying in baby talk, cuddle time with another person