In the lyrics of a song, the text goes
swing a little more, little more o’er the merry-o
I know the proverb "the more the merrier", but
o'er is apparently an archaic form of
over, which confuses me.
This line is followed by a very similar one, which might help:
Swing a little more, little more o'er the merry-o
Swing a little more, a little more next to me
"Swing a little more" is the singer telling the girl to keep dancing. You can ignore the repetition of 'little more' as that's just poetry.
The end of each line is the singer telling her where to dance. "Next to me" is obvious enough. As you discovered, "o'er" is an archaic form of "over", but this kind of archaic language often appears in folk music and folk-based music (Flogging Molly play a kind of folk-punk). So the singer wants her to dance "over the merry-o".
Which brings us to the question of what a merry-o is, and how one dances over it. But at this point we've left the realms of English and entered 'mouth music'. Many folk songs include sections of meaningless words and sounds. A well known example is the line "wack fol di daddy-o" from the song Whiskey In The Jar.
So unless someone else knows better, I would assume that "o'er the merry-o" is a section of mouth music and not intended to mean anything.