Someone who is hazed or confused or dizzy is often said to be dazed. They see your groggy because you might be drunk from the grog. Back in the 18th century, a British Admiral E. Vernon tried to change the drinking habits of his sailors by modifying their rum with more water in it. So it would prevent them from getting too drunk. The old admiral use to wear a grogram coat and was known as Old Grog. Grog was often used to describe rum but not so often these days.
Also a nice fact is that George Washington’s brother Lawrence Washington was on one of Vernon’s ships. Though he wasn’t George’s actual brother but rather his half brother.