Etymology

Formed within English on tite (adv.).

PGmc Ancestor

*tīða- 

Proposed ON Etymon (OIcel representative)

tíðr (adj.) ‘frequent, usual, customary’
(ONP tíðr (2) (adj.))

Other Scandinavian Reflexes

OE Cognate

cp. tīd (n.) ‘time’

Phonological and morphological markers

ON consonant cluster assimilation

<p>ON adjectival (adverbial) <em>-t</em></p>

Summary category

A3*c

Attestation

Similarly to tite (adv.), many, but not all, attestations of this form of the adv. come from alliterative texts, although the first attestation is from Sir Tristrem (in rhyming position) in the early 14c. 

Occurrences in the Gersum Corpus

WA 267, 738*, 888 etc.

The D MS of WA has tyte (tite (adv.)) at 1875.

Bibliography

MED tītelī (adv.) , OED3 titely (adv.) , HTOED ; see further tite (adv.).