symmetry vs counterbalance

symmetry and counterbalance both are nouns.

Word	Noun	Adjective	Verb	Adverb
symmetry	Yes	No	No	No
counterbalance	Yes	No	Yes	No

As nouns, counterbalance is a hypernym of symmetry; that is, counterbalance is a word with a broader meaning than symmetry:

Other hypernyms of symmetry include balance, equilibrium, equipoise.

symmetry (noun)	counterbalance (noun)
(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
(physics) the property of being isotropic; having the same value when measured in different directions	a compensating equivalent
balance among the parts of something	equality of distribution

symmetry (verb)	counterbalance (verb)
	oppose and mitigate the effects of by contrary actions
	contrast with equal weight or force
	adjust for