proportion vs balance

proportion and balance both are nouns.

Word	Noun	Adjective	Verb	Adverb
proportion	Yes	No	Yes	No
balance	Yes	No	Yes	No

As nouns, proportion and balance are synonyms defined as:

proportion and balance: harmonious arrangement or relation of parts or elements within a whole (as in a design)

Other synonyms of proportion include proportionality.

As nouns, balance is a hypernym of proportion; that is, balance is a word with a broader meaning than proportion:

Other hypernyms of proportion include counterbalance, equilibrium, equipoise.

proportion (noun)	balance (noun)
magnitude or extent	a scale for weighing; depends on pull of gravity
harmonious arrangement or relation of parts or elements within a whole (as in a design)	a weight that balances another weight
the quotient obtained when the magnitude of a part is divided by the magnitude of the whole	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
the relation between things (or parts of things) with respect to their comparative quantity, magnitude, or degree	harmonious arrangement or relation of parts or elements within a whole (as in a design)
balance among the parts of something	(mathematics) an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane
	equality between the totals of the credit and debit sides of an account
	the difference between the totals of the credit and debit sides of an account
	something left after other parts have been taken away
	equality of distribution
	a state of equilibrium

proportion (verb)	balance (verb)
adjust in size relative to other things	hold or carry in equilibrium
give pleasant proportions to	compute credits and debits of an account
	bring into balance or equilibrium
	be in equilibrium