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
Synonyms, antonyms and the broader and narrower relations for balance come from Princeton University’s WordNet. Full sources and licences.