My theory is it's from the perspective of a young girl speaking on behalf of her friends about this one girl (the Belle of Belfast city) who's got the attention of all the boys in town. She hopes when she goes home, the boys "won't leave the girls alone" "Let the boys stay as they will" even though "they pull my hair and stole my comb, that's alright" because it means they're not chasing after this one girl who's "handsome, pretty, nice as apple pie" etc. and "courting, one two three", taking up the time of all the boys so there's none left for the girl singing the song.
Not only that, but she's speaking on behalf of her friend, Old Jonny Mary, who "says she'll die if she doesn't get the fella with the roving eye.", she has no hope cause this guy is known for checking out other women all the time anyway (his "roving eye").
But it gets worse - the singer of the song knows that when this girl finally does decide on a "lad of her own", "she won't tell her ma till she comes home", meaning she's not going to tell anyone she's decided on just one yet, she's going to keep stringing them all along. The singer names Albert Mooney as the one she's actually interested in all along. So even though this Bell of Belfast is only really serious about one guy, Albert, she's still going to string all the others along, taking away attention from all the other girls.