Etymology

Formed in English on grayþe (adj.), but cp. also grayþe (v.). 

PGmc Ancestor

*ga-raið-a

Proposed ON Etymon (OIcel representative)

greiðr (adj.) ‘ready, free’ 
(ONP greiðr (adj.))

Other Scandinavian Reflexes

OE Cognate

gerǣde (adj.) 'ready'

Phonological and morphological markers

ON /ei/ < PGmc */ai/

syncope

Summary category

A1*c

Attestation

The adv. is comparatively rare and most citations in MED are from 15c N texts. See also grayþe (adj.) and grayþe (v.). 

Occurrences in the Gersum Corpus

WA 3689

The instance at WA 3689 has also been interpreted as the pp. of the grayþe (v.). The sense required by the context at WA 3689 ( 'and þat was grauen all grayd of gilden platis') perhaps requires a greater extension of the sense of the adj. (MED suggests 'fairly, beautifully' and Skeat WA 'excellently') than other uses of the adv., e.g. MED's (1a) 'quickly, at once' and (1b) 'exactly, carefully'.

Bibliography

MED greith (adv.) , OED graith (adj. and adv.) , HTOED ; see further grayþe (adj.).