Old English gewiht "weighing, weight, downward force of a body, heaviness," from Proto-Germanic *wihti- (source also of Old Norse vætt, Danish vegt, Old Frisian wicht, Middle Dutch gewicht, German Gewicht), from *weg- (see weigh).
Figurative sense of "burden" is late 14c. To lose weight "get thinner" is recorded from 1961. Weight Watcher as a trademark name dates from 1960. To pull one's weight (1921) is from rowing. To throw (one's) weight around figuratively is by 1922. Weight-training is from 1945. Weight-lifting is from 1885; weight-lifter (human) from 1893.
mid-15c., "significant, of much import, bearing weight or consequence," from Medieval Latin importantem (nominative importans) "important, momentous," present-participle adjective from importare "be significant in," from Latin importare "bring in, convey, bring in from abroad," from assimilated form of in- "into, in" (from PIE root *en "in") + portare "to carry," from PIE root *per- (2) "to lead, pass over." The meaning "pretentious, pompous" is from 1713. Related: Importantly. Compare import (v.) and (n.).