Definition of "batty"

On Sunday’s David Frost Show, Baroness Thatcher looked quite batty to me, eyes rolling.

1992 July 6, Edwina Currie, Diary

And from each other look thou lead them thusTill o'er their brows death-counterfeiting sleepWith leaden legs and batty wings doth creep.

c. 1595–1596 (date written), William Shakespeare, “A Midsommer Nights Dreame”, in Mr. William Shakespeares Comedies, Histories, & Tragedies: Published According to the True Originall Copies (First Folio), London: […] Isaac Iaggard, and Ed[ward] Blount, published 1623, (please specify the act number in uppercase Roman numerals, and the scene number in lowercase Roman numerals)

He kick the boy down and beat the boy back and batty and leg.

2014, Marlon James, A Brief History of Seven Killings, Oneworld Publications (2015), page 35

For example, recent Jamaican 'raga' lyrics by Buju Banton and Brand Nubian attach the affirmation of black identity to crude animosity towards homosexuality and contain offensive language against the 'batties' as icons of non-blackness.

1996, Rudi Bleys, The geography of perversion