Etymology

ME at as an infin. marker must be a reflex of the prep. PGmc *at, as in OE æt and OIcel at (and cp. Go at, OFris et, OS at, OHG az) (and see also at (prep.)). As OED remarks, the usage in English is not quite identical to that in the Scand languages (in English, it is found mainly with infinitives of purpose, rather than more generally); but, esp. given the northern distribution of ME and MnE dial at in this role, most authorities adduce some ON input.

PGmc Ancestor

*at

Proposed ON Etymon (OIcel representative)

at ‘to, (in order) to’
(ONP at (5) (nota infinitivi))

Other Scandinavian Reflexes

Icel að, Dan at, Sw åt

OE Cognate

æt 'at, near, by, in (etc.)'

Phonological and morphological markers

Summary category

C3c

Attestation

Mainly N and NM in ME, and N in MnE dialect usage.

Occurrences in the Gersum Corpus

WA 636, 872, 1103

The A MS of WA has another apparent instance at 2178, but this is altered to to (on the basis of a scribal insertion) by TPD in their emendation of this line (their 2305).

Bibliography

MED at (adv. with infinitive), OED at (prep.) (sense VI (39)), Bj. 201, de Vries at (2), Mag. að (3), Orel *at, Kroonen *at, AEW æt (1), DOE æt (prep. and adv.)