rudder (n.)

"a load, that which is borne or carried," Old English byrðen "a load, weight, charge, duty;" also "a child;" from Proto-Germanic *burthinjo- "that which is borne" (source also of Old Norse byrðr, Old Saxon burthinnia, German bürde, Gothic baurþei), from PIE root *bher- (1) "to carry," also "to bear children."

The shift from -th- to -d- began early 12c. (compare murder (n.), rudder, afford). Archaic burthen is occasionally retained for the specific sense of "capacity of a ship." Beast of burden is from 1740. Burden of proof (Latin onus probandi) "obligation on one party in an action to establish an alleged fact by proof" is recorded from 1590s.

Middle English fader, from 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).

This is from the PIE root *pəter- "father" (source also of Sanskrit pitar-, Greek pater, Latin pater, Old Persian pita, Old Irish athir "father"), which is presumably from baby-speak sound "pa." The ending formerly was regarded as an agent-noun affix. The classic example of Grimm's Law, where PIE "p-" becomes Germanic "f-."

The spelling with -th- (15c.) reflects a widespread phonetic shift in Middle English that turned -der to -ther in many words, perhaps reinforced in this case by Old Norse forms; the spelling caught up to pronunciation in 1500s (compare mother (n.), weather (n.), hither, gather).

As a title of various Church dignitaries from c. 1300; the 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.

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]