Etymology

cp. OIcel beiða ‘to ask for, demand, summon, provoke, desire’ < PGmc *baiðjan-; cp. OE bǣdan ‘to compel’, Go báidjan, OS bēdian, OHG beiten. The sense 'to grant' in Gaw could have been promoted by analogy with ME beden, 'to ask for, summon, offer, present', or less likely a ME word derived from ON  beina, 'to further, help, serve' . 

PGmc Ancestor

*baiðjan-

Proposed ON Etymon (OIcel representative)

beiða ‘to ask for, demand, summon, provoke, desire’ 
(ONP beiða (vb.))

Other Scandinavian Reflexes

Far beiða, Icel beiða, Norw beidast, ODan bethæs, Sw bedas

OE Cognate

bǣdan, 'to impel, solicit, afflict' 

Phonological and morphological markers

ON /ei/ &lt; PGmc */ai/

ON fricative /&eth;/ &lt; PGmc */&eth;/

Summary category

A1*c

Attestation

Found only in Gaw, Erk and (by emendation) in c1325 Ichot a burde in a bour ase beryl so bryht (Hrl 2253) 35, the dialect of which Brook (1933:60) identified as NWM (see also Putter 2013).

Occurrences in the Gersum Corpus

Gaw 327, 1404, 1840; Erk 257

MED's sense (a) 'to inquire, ask', closest to the original sense of the ON, only occurs in Erk (see TGD 327n).

Bibliography

MED baithen (v.) , OED baithe (v.) , HTOED , Dance bayþe, Bj. 41, 161, de Vries beiða (2), Mag. beiða, Orel *baiðjanan, Kroonen *baidjan-, AEW bǣdan