What word or phrase does your mother always say?
1770, "drunk," from grog + -y (2). Non-alcoholic meaning "shaky, tottering" is from 1832, originally from the fight ring. Related: Groggily; grogginess.
Sleepy; dazed; semiconscious: Conlon was so groggy that he wanted to know why Nelson was not coaching the Warriors (1832+)