From the second edition (1989):
pigsney, -ny
Forms: α. 4 piggesneyȝe, 4–6 piggesnye, 6 pyggysny, pygges nye, pigges-ny, pygs(-)nie, pygsnye, pigesnie, 6–8 pigs(-)nye, 7 pigsneye, pignie, 8 pig-nye, 6– pigsny, pigs(-)nie, pigs(-)ney; β. 6 pigseie, 9 (dial.) pigsy. [ME. f. pigges pig's + neyȝe, var. of eyȝe, eye with prosthetic n, app. derived from an eye, min eye; prob. originating in children's talk and the fond prattle of nurses.
The eye of the pig (as that of a bird in bird's-nie) is taken as a familiar type of a small eye; the expression is thus equivalent to pinke or pinkie nye, pinkeny, ‘tiny eye’, which was used in the same way as a term of endearment; but early examples showing pigges nye applied to the eye itself (sense 2) have not yet been found.]

1. One specially cherished; a darling, pet; commonly used as an endearing form of address. a. Chiefly applied to a girl or woman; in mod. dial. often opprobrious.

α c1386 Chaucer Miller's T. 82 She was a prymerole a piggesnye ffor any lord to leggen in his bedde. a1529 Skelton Womanhod, etc. 20 What prate ye, praty pyggysny? 1549 Chaloner Erasm. on Folly Fij, Another fall in love with some yonge pygsnie. a1553 Udall Royster D. i. iv. (Arb.) 27 Then ist mine owne pygs nie, and blessing on my hart. 1589 Triumphs Love & Fort. Fijb, Then will I make my loving song upon mine owne pigsnye. 1629 Massinger Picture ii. i, If thou art, As I believe, the pigsney of his heart, Know he's in health. 1667 Dryden Tempest iv. iii, How does my Pigs-nye? 1698 Farquhar Love & Bottle i. i, And the little pigsny has mamma's mouth. 1784 R. Bage Barham Downs I. 11 Never think I shall long survive thee, pigsnye. 1834 Southey Doctor liv. (1848) 121/2 When pigsnie arrives and the purchaser opens the close sedan chair in which she has been conveyed to his house. 1876 O. Madox-Brown Dwale Bluth i. v. 102 She began to pour forth‥insinuations relative to a certain ‘Trapseing, hautecking, kerping, pigsnie’.
β 1553 Bale tr. Gardiner's De vera Obed. Kjb, How doth my sweteheart, what saith now pigges eye? 1869 J. P. Morris Gloss. Words Furness 71 Pigsy, a term of endearment, as ‘Thow lile pigsy’.

b. More rarely applied to a man or boy. Obs.

1581 J. Bell Haddon's Answ. Osor. 68b, And your sweet piggesnye Emanuel will smoyle close in his sleave. a1588 Tarlton Jests (1844) Introd. 21 The player fooles deare darling pigsnie He calles himselfe his brother. 1708 Brit. Apollo No. 68. 2/2 You, ven once they have your Money, No more their Pigsnies are nor Honey.

2. An eye; a ‘dear little eye’. Obs.

1663 Butler Hud. ii. i. 560 And shine upon me but benignly, With that one, and that other Pigsneye. 1709 Brit. Apollo II. No. 11. 3/1, I rise, And rub my Pigs Nyes. a1774 Goldsm. tr. Scarron's Com. Romance (1775) II. 10 The hostess received such a blow on her little pig-nyes, that she saw a hundred thousand lights at the same time.