burden (n.2) Look up burden at Dictionary.com
"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.
burden (n.1) Look up burden at Dictionary.com
"a load," 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 bear, to carry; give birth" (see infer).

The shift from -th- to -d- took place beginning 12c. (compare murder (n.), rudder, afford). Archaic burthen is occasionally retained for the specific sense of "capacity of a ship." Burden of proof is recorded from 1590s.