father-in-law n.

Old English fæder "he who begets a child, nearest male ancestor;" also "any lineal male ancestor; the Supreme Being," and by late Old English, "one who exercises parental care over another," from Proto-Germanic *fader (source also of Old Saxon fadar, Old Frisian feder, Dutch vader, Old Norse faðir, Old High German fatar, German vater; in Gothic usually expressed by atta), from PIE *pəter- "father" (source also of Sanskrit pitar-, Greek pater, Latin pater, Old Persian pita, Old Irish athir "father"), presumably from baby-speak sound "pa." The ending formerly was regarded as an agent-noun affix.

My heart leaps up when I behold

  A rainbow in the sky:

So was it when my life began;

So is it now I am a man;

So be it when I shall grow old,

  Or let me die!

The Child is father of the Man;

I could wish my days to be

Bound each to each by natural piety.

[Wordsworth, 1802]

The classic example of Grimm's Law, where PIE "p-" becomes Germanic "f-." Spelling with -th- (15c.) reflects widespread phonetic shift in Middle English that turned -der to -ther in many words, perhaps reinforced in this case by Old Norse forms; spelling caught up to pronunciation in 1500s (compare mother (n.), weather (n.), hither, gather). As a title of various Church dignitaries from c. 1300; meaning "creator, inventor, author" is from mid-14c.; that of "anything that gives rise to something else" is from late 14c. As a respectful title for an older man, recorded from 1550s. Father-figure is from 1954. Fathers "leading men, elders" is from 1580s.

1894, "anyone of a relationship not natural," abstracted from father-in-law, etc.

The position of the 'in-laws' (a happy phrase which is attributed ... to her Majesty, than whom no one can be better acquainted with the article) is often not very apt to promote happiness. [Blackwood's Magazine, 1894]

The earliest recorded use of the formation is in brother-in-law (13c.); the law is Canon Law, which defines degrees of relationship within which marriage is prohibited. Thus the word originally had a more narrow application; its general extension to more distant relatives of one's spouse is, according to OED "recent colloquial or journalistic phraseology." Middle English inlaue (13c.) meant "one within or restored to the protection and benefit of the law" (opposite of an outlaw), from a verb inlauen, from Old English inlagian "reverse sentence of outlawry."