Green’s Dictionary of Slang

1. a promiscuous woman, a prostitute.

1611		Middleton No Wit or Help like a Womans (1657) IV i: The Mother of her was a good twigger the whilst.
1612		Pasquil’s Night-cap (1877) 32: Now, Benedicite, her Mother said, And hast thou bene already such a Twigger.
1696		Motteux (trans.) Pantagruelian Prognostications (1927) II 694: Those whom Venus is said to rule, as punks, jilts, [...] wag-tails, cockatrices, whipsters, twiggers, harlots.

2. a womanizer.

1594

Nashe Dido, Queen of Carthage in Works VI (1883–4) IV v: Go, you wagge, / You’ll be a twigger when you come to age.