One reeling, and ready to fall at the least touch; also the childish amusement of riding upon the two ends of a plank, poised upon the prop underneath its centre, called also see-saw. Perhaps tatter is a rustic pronunciation of totter.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
To Titter * Tittle-tattleNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes