Etymology

 ME rawþe is a derivation on the PGmc root *xrew-, most simply explained as an indigenous creation on the stem of the OE v. hrēowan ‘to distress, grieve; regret (impers.); repent’ or the adj. hrēow ‘sorrowful, repentant’, formed using the affix *-iþō.  (thus TGD, GDS, and see also Holthausen 1923: 135). There is a tradition in the etymological scholarship (esp. early on) of explaining ME rawþe as a calque modelled on the ON n. represented by OIcel hryggð ‘affliction, grief, sorrow’ (thus e.g. Skeat 1892: 467, TG , Gollancz ed. Pearl, OED and MED), presumably because OE already had a n. hrēow formed on this root (cp. OFris riowa, OS hriwi, and for the ME reflex see MED s.v. reu(e n.1)), and because an equivalent in -þ is not otherwise attested in WGmc. 

PGmc Ancestor

*xrew-

Proposed ON Etymon (OIcel representative)

hryggð ‘affliction, grief, sorrow’
(ONP hryggð (sb.))

Other Scandinavian Reflexes

Icel hryggð, Norw rygd

OE Cognate

cp. hrēowan (v.) ‘to distress, grieve; regret (impers.); repent’, hrēow (adj.) ‘sorrowful, repentant’; cp. hrēow 'sorrow, regret'

Phonological and morphological markers

Summary category

CCC1c

Attestation

Frequent and widespread from early ME (inc. the Lamb.Hom. and Trin.Hom.).

Occurrences in the Gersum Corpus

Gaw 2204, Pe 858; Cl 233, 972; Pat 21, 284, 396; Erk 240; WA 1280, 2244, 2813 etc.

On the sense of Gaw 2204 ‘a grievous thing’ see Vant 2204n. On the sense of Erk 240, see Peterson 240n. The D MS of WA has <rathe> at 2824, though TPD (2949n) note that the A MS reading <rauth> fits with the sense of the context. 

Bibliography

MED reuth(e (n.) , OED3 ruth (1) , HTOED , HTOED , HTOED , Dance rawþe, Bj. 72, de Vries hrygð, Mag. hryggur (2)