Etymology

Two different identifications have been offered for this word in the context of Gaw 1461 (‘Þen, braynwod for bate, on burnez he [the boar] rasez’): (1) The more probable, favoured by most editors, is to read bate as an instance of ME bate ‘discord, dissention, disagreement (etc.); armed conflict, combat, battle’ derived <  the OFr stem -bat or -batre, either formed on the related v. ME baten in the sense ‘to engage in combat, fight’ (< OFr batre, < late Lat bat(t)ere) or a shortened form of ME debate ‘quarrel, dispute, disagreement’ (etc.) (< the same stem); cp. AN batre ‘beating; assault, battery; threshing’, bat ‘debate, discussion’. This would account for both the form of the word and the sense in context. (2) GDS (followed by Vant (1461n) and in part MED) instead glosses bate here as ‘baiting’, and adduces ON beit and OE bāt without further comment, suggesting some sort of connection with the ON-derived ME bait ‘bait for fish or fowl; a worm or insect to be used for bait; a lure or enticement’ (PDE bait) (the best OIcel nominal comparandum in terms of sense is OIcel beita (fem.) ‘bait’; cp. beit (fem.), beiti (neut.) 'grazing, pasture'), or with the related v. ME baiten esp. in the senses ‘to bait (an animal) with an attacking or herding dog’ (etc.), ‘to harass, torment, or persecute’ < the ON v. represented by OIcel beita (lit. ‘to cause to bite’, but here see esp. ONP’s sense (3) ‘to chase (with animals), hunt (with animals), set (animals) on’); cp. OE bǣtan in DOE’s sense (3) ‘to bait, set with animals upon’ (ÆLS (Agatha) only), OS und-bētian ‘to dismount’, OHG beizen ‘to spurn on’, < PGmc *baitjan- the causative of *bītan- ‘to bite’. With the OIcel nouns cp. MHG beiz(e) ‘hunting’; OE bāt ‘food’ (which actually seems to be a ghost-word). ME bate at Gaw 1461 would then be native in form (< an OE *bāt) but show some semantic influence from the ON-derived ME bait-. 

PGmc Ancestor

(2) *bait-

Proposed ON Etymon (OIcel representative)

(2)  beita ‘bait’; cp. beita (v.) ‘to cause to bite’; ‘to chase (with animals), hunt (with animals), set (animals) on’ (etc.), beit, beiti 'grazing, pasture'
(ONP (2) beit (1) (sb.), beita (1) (sb.), beita (2) (vb.), beiti (1) (sb.))

Other Scandinavian Reflexes

(2) Far beita, Icel beita, Norw beite, beita, ODan bēd, Sw bete

OE Cognate

(2) *bāt 'food'

Phonological and morphological markers

Summary category

DD2

Attestation

(1) ME bate ‘discord’ (etc.) is found from the late 14c. onwards, with no strong dial or generic colouring to its distribution.  (2) This would be a hapax legomenon in this form (ME bait ‘bait’ is fairly widespread from the late14c.; the corresponding v. is known since Orrm, earliest in N/E texts but distributed more broadly from the late 14c.).

Occurrences in the Gersum Corpus

Gaw 1461

Bibliography

MED bāte (n.2) , OED bate (n.1) , HTOED , Dance bate; (1) OED bate (n.1) , MED bāte (n.1) , AND bat (2); batre (2), FEW battuere, DEAF bat (1) (s.); batre (v. tr.); (2) de Vries beita (1); beita (2), Mag. beita (1); beita (2), Seebold beit-a-, Orel *baitjanan, OED bait (n.1) ; bait (v.1), MED bait (n.) ; baiten (v.), AEW bǣtan, DOE bǣtan, Bj. 41