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Here are the OED etymological notes for right (adj.)
Broadly the same range of meanings is found in all of the early Germanic languages; however, senses relating to the right-hand side (of the human body, etc.) appear to be restricted to West Germanic languages, and are not common in the earliest stages even of these, hence they seem likely to show secondary developments (compare swither adj. for the usual word in Old English, and see dexter adj. for the evidence for an Indo-European word with this meaning). In Old English this meaning is recorded only in right hand n., in which the word probably referred originally to the perception that the right hand was the stronger and the more appropriate for most tasks. (In a number of the Romance languages the same meaning has also developed in a derivative of classical Latin rectus, ultimately from the same base; compare French droit, Catalan dret, Spanish derecho, Portuguese direito, Romanian drept < classical Latin dīrectus.)
On the form history see discussion at right n. The Old English (Anglian) form ræht (apparently showing a reflex of the Anglian smoothed form reht : see α. forms) has not been satisfactorily explained; compare cnæht and gefæht , Anglian variants respectively of knight n. and fight n., and see further A. Campbell Old Eng. Gram. (1959) §227 note 2.
In Old English frequent as the first element in compounds, some of which provide the earliest attestation of particular senses (compare senses A. 8a, A. 9, A. 14a).
Probably influenced semantically in a number of senses by association with classical Latin rectus rect adj. (especially in the technical uses at sense A. 2) and with Anglo-Norman and Old French, Middle French, French droit .
Here are the OED etymological notes for right (n.)
Cognate with or formed similarly to Old Frisian riucht (West Frisian rjocht , rjucht ), Old Dutch reht (Middle Dutch recht , Dutch recht ), Old Saxon reht (Middle Low German recht ), Old High German reht (Middle High German reht , German recht ) < the Germanic base of right adj. Compare also Old Icelandic réttr , Old Swedish rätter (Swedish rätt ), Old Danish ræt (Danish ret ), which reflect a different formation (u -stem) ultimately < the same Germanic base. In some senses (especially sense 15 and Phrases 3) probably also partly aphetic < i-riht n.
In Old English a strong neuter (a -stem); the prefixed form geriht i-riht n. is also commonly attested. The early Kentish form reoht (see α. forms) shows regular breaking of short e before a velar fricative, while the regular Anglian form reht (see α. forms) shows smoothing of the diphthong. In West Saxon, on the other hand, monophthongization and raising before a palatalized fricative followed by a dental consonant (palatal mutation) resulted in the form riht or (with laxed vowel after r ) ryht (originally only word-finally or if followed by a front vowel, but apparently soon extended analogically to such forms as genitive plural rihta ), a change that is also attested in later Kentish sources. Such forms gradually spread northwards in late Old English and early Middle English (compare Older Scots richt beside less frequent recht ). See further A. Campbell Old Eng. Gram. (1959) §§304–11, R. M. Hogg Gram. Old Eng. (1992) I. §§5.113–18, R. Jordan Handb. der mittelenglischen Grammatik (1934) §69.
In Middle English the semantic development was probably influenced by similar developments shown by Anglo-Norman and Old French dreit , Anglo-Norman and Old French, Middle French droit droit n.1, as were a number of phrasal constructions.