birthright (n.)

c. 1200, "fact of being born;" mid-13c., "act of giving birth, a bringing forth by the mother, childbirth," sometimes in Middle English also "conception;" also "that which is born, offspring, child;" from a Scandinavian source such as Old Norse *byrðr (replacing cognate Old English gebyrd "birth, descent, race; offspring; nature; fate"), from Proto-Germanic *gaburthis (source also of Old Frisian berd, Old Saxon giburd, Dutch geboorte, Old High German giburt, German geburt, Gothic gabaurþs), from PIE *bhrto past participle of root *bher- (1) "to carry; to bear children" (compare bear (v.)).

Suffix -th is for "process" (as in bath, death). Meaning "condition into which a person is born, lineage, descent" is from c. 1200 (also in the Old English word). In reference to non-living things, "any coming into existence" is from 1610s. Birth control is from 1914; birth certificate is from 1842.

Old English riht (West Saxon, Kentish), reht (Anglian), "that which is morally right, duty, obligation," also "rule of conduct; law of a land;" also "what someone deserves; a just claim, what is due, equitable treatment;" also "correctness, truth;" also "a legal entitlement (to possession of property, etc.), a privilege," from Proto-Germanic *rehtan (see right (adj.1)). In Middle English often contrasted to might or wrong. From early 14c. as "a right action, a good deed," hence the right "that which is just or true, righteousness."

From what has been said it will be seen that the adjective right has a much wider signification than the substantive Right. Every thing is right which is conformable to the Supreme Rule of human action ; but that only is a Right which, being conformable to the Supreme Rule, is realized in Society, and vested in a particular person. Hence the two words may often be properly opposed. We may say that a poor man has no Right to relief, but it is right he should have it. A rich man has a Right to destroy the harvest of his fields, but to do so would not be right. [William Whewell, "Elements of Morality," 1858]

The meaning "the right hand or right side" (as opposed to the left) is from mid-13c.; see right (adj.2) for sense development. As "the right wing of an army" by 1707. Political use is from 1825. Meaning "a blow with the right fist" is from 1898; the meaning "a right-hand turn" is by 1961. The phrase to rights "at once, straightway" is 1660s, from an earlier meaning "in a proper manner" (Middle English). Adjectival phrase right-to-work is attested from 1958; right-to-die by 1976. To do or something in one's own right (1610s) is from the legal use for "title or claim to something possessed by one or more" (12c.).