WordNet sense 1 (equality of distribution):

counterbalance, equilibrium, equipoise

WordNet sense 2 (something left after other parts have been taken away):

remainder, residual, residue, residuum, rest

WordNet sense 3 ((astrology) a person who is born while the sun is in Libra):

Libra

WordNet sense 4 (the seventh sign of the zodiac; the sun is in this sign from about September 23 to October 22):

Libra the Balance, Libra the Scales

WordNet sense 5 (harmonious arrangement or relation of parts or elements within a whole (as in a design)):

proportion, proportionality

WordNet sense 6 ((mathematics) an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane):

correspondence, symmetry, symmetricalness

WordNet sense 7 (a weight that balances another weight):

counterpoise, counterweight, equalizer, equaliser

WordNet sense 8 (a wheel that regulates the rate of movement in a machine; especially a wheel oscillating against the hairspring of a timepiece to regulate its beat):

balance wheel

WordNet sense 9 (bring into balance or equilibrium):

equilibrate, equilibrise, equilibrize

WordNet sense 10 (hold or carry in equilibrium):

poise, poise