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"a load," Old English byrðen "a load, weight, charge, duty;" also "a child;" from Proto-Germanic *burthinjo- "that which is borne" (cf. Old Norse byrðr, Old Saxon burthinnia, German bürde, Gothic baurþei), from PIE root *bher- (1) "to bear, to carry; give birth" (see infer).
The shift from -th- to -d- took place beginning 12c. (cf. murder). Archaic burthen is occasionally retained for the specific sense of "capacity of a ship." Burden of proof is recorded from 1590s.
"leading idea," 1640s, a figurative use from earlier sense "refrain or chorus of a song," 1590s, originally "bass accompaniment to music" (late 14c.), from Old French bordon "bumble-bee, drone," or directly from Medieval Latin burdonom "drone, drone bass" (source of French bourdon, Spanish bordon, Portuguese bordão, Italian bordone), of echoic origin.
(1.) A load of any kind (Ex. 23:5). (2.) A severe task (Ex. 2:11). (3.) A difficult duty, requiring effort (Ex. 18:22). (4.) A prophecy of a calamitous or disastrous nature (Isa. 13:1; 17:1; Hab. 1:1, etc.).