It is meaningless, but Triona was a notorious mumbler in those days (her accent wasn't strong, but her enunciation was poor) and it was sometimes impossible to make out what she was singing. 'Wedding class' is certainly a mis-hearing of something else; probably, as has been suggested (and which is supported by traditional versions) 'wee town clerk[s]'. Whether she or whoever she learned it from had garbled the words, or whether it just sounded that way, I wouldn't care to guess.