Tarry in the context of the song lyric quoted seems to mean "waited, hung around," that sort of thing.

One often sees quaint (pseudo) little notices saying things like, "Tarry a while" inviting the traveller to stop and rest (and buy a drink!)

I suppose it means much the same as 'dally'.   It's a perfectly normal English word. It's not in every day use, and would now be used for effect because it is slightly archaic.

Concise Oxford Dictionary has "archaic or literary: defer coming or going; linger, stay, wait; be tardy. Middle English, origin uncertain."

(Also 'Tarry' with a long 'a' "of or like or smeared with tar.") ;0)