Old English beran "to carry, bring; bring forth, give birth to, produce; to endure without resistance; to support, hold up, sustain; to wear" (class IV strong verb; past tense bær, past participle boren), from Proto-Germanic *beranan (source also of Old Saxon beran, Old Frisian bera "bear, give birth," Middle Dutch beren "carry a child," Old High German beran, German gebären, Old Norse bera "carry, bring, bear, endure; give birth," Gothic bairan "to carry, bear, give birth to"), from PIE root *bher- (1) "carry a burden, bring," also "give birth" (though only English and German strongly retain this sense, and Russian has beremennaya "pregnant").
Old English past tense bær became Middle English bare; alternative bore began to appear c. 1400, but bare remained the literary form till after 1600. Past participle distinction of borne for "carried" and born for "given birth" is from late 18c.
Many senses are from notion of "move onward by pressure." From c. 1300 as "possess as an attribute or characteristic." Meaning "sustain without sinking" is from 1520s; to bear (something) in mind is from 1530s; meaning "tend, be directed (in a certain way)" is from c. 1600. To bear down "proceed forcefully toward" (especially in nautical use) is from 1716. To bear up is from 1650s as "be firm, have fortitude."