Then sigh not so,
But let them go,
And be you blithe and bonny;
Converting all your sounds of woe
Into Hey nonny, nonny.
Sigh No More, Ladies...
from Much Ado about Nothing, by William Shakespeare
In the 1500s through the 1600s, and decreasingly so well into the mid-1800s, nonny-nonny, nonny-no, and other related bits of reduplicated babbling were important phrases in the art of song composition. These forms were used as part of a song's refrain, giving the songwriter an easy few lines and helping the audience sing along. However, the subtext was as important as the rhythm and meter, as nonny-nonny and its kin were indicators of ribald content, and were used to cover up indelicate phrases.
Cupid bidds itt shold bee soe,
Because all men were made for her hinononino.
Downe: Sate the Shepard
From Loose and Humorous Songs, edited by Frederick James Furnivall.
It didn't take long for the phrase to start to be used metaphorically, as in the Shakespeare quote above; 'hi nonny-nonny' and its ilk were used to refer to partying, ribald behavior, and carefree carelessness in action and demeanor. From John Fletcher's "That noble mind to melt away and moulder, For a hey nonny, nonny." (1605) to Leigh Hunt's "Ah little ranting Johnny, Forever blithe and bonny, And singing nonny, nonny," (1832), the nonny-nonnies were popularly used as a reference to bawdy songs and partying, in addition to being parts of the songs.
Who ever heard thy pipe and pleasing vaine,
And doth but heare this scurrill minstralcy,
These noninos of filthie ribauldry,
that doth not muse.
The Idea: the Shepheards Garland - Third Eglog
by Michael Drayton, 1593