balance has 25 distinct synonyms spread across 10 of its 16 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its 2 recorded opposites are imbalance, unbalance.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
a state of equilibrium
equality between the totals of the credit and debit sides of an account
harmonious arrangement or relation of parts or elements within a whole (as in a design)
“in all perfectly beautiful objects there is found the opposition of one part to another and a reciprocal balance”
equality of distribution
the difference between the totals of the credit and debit sides of an account
the seventh sign of the zodiac; the sun is in this sign from about September 23 to October 22
(mathematics) an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane
a weight that balances another weight
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
a scale for weighing; depends on pull of gravity
bring into balance or equilibrium
“She has to balance work and her domestic duties”
Synonyms, antonyms and the broader and narrower relations for balance come from Princeton University’s WordNet. Full sources and licences.
compute credits and debits of an account
be in equilibrium
“He was balancing on one foot”