Does "courtesy of me" means "I offer you a drink" here?
Native speaker’s answer
Rebecca
Yes. "Courtesy of me" means "provided by" or "as a result of a particular thing or situation." It's a gift from someone else that would usually need to be paid for, but it's offered for free. Ex: She got a free ice cream cone courtesy of the Dairy Queen Manager. Ex: These drinks are courtesy from those gentlemen over there. Ex: Two free tickets to the game, courtesy of Verizon.