Green’s Dictionary of Slang

1. infected with a venereal disease [pun on SE burned/burned adj.¹ (1)].

c.1602		Shakespeare Troilus and Cressida I iii: The Grecian dames are sunburnt, and not worth the splinter of a lance.
1725		New Canting Dict. n.p.: sun-Burnt, clapt.
1737, 1759, 1760, 1776		Bailey Universal Etym. Eng. Dict. [as cit. 1725].
1785, 1788, 1796		Grose Classical Dict. of the Vulgar Tongue.
1811		Lex. Balatronicum.
1823		Egan Grose’s Classical Dict. of the Vulgar Tongue.

2. drunk.

1611

L. Barry Ram-Alley IV i: That’s all the fault Old Iustices haue, where they are at feasts, They will bib hard, they will be fine Sun-burnt, Sufficent, foxt, or Columberd now and than.