Counterbalances rhymes with:
benevolences, imbalances, silences, absences, acceptances, acquaintances, alliance's, allowances, annoyances, assurances, benevolences, cadences, clearances, coincidences, conference's, confidences, continuances, contrivances, conveniences, countenances, differences, disallowances, disappearances, divergences, eminences, experiences, florence's, hindrances, imbalances, incidences, inconveniences, independence's, influences, insurance's, insurances, issuances, lawrence's, licences, licenses, nuisances, observances, occurrences, ordinances, ordnance's, outdistances, preferences, presences, providence's, province's, reassurances, references, reliance's, remembrances, reminiscences, remittances, residences, science's, sciences', silences, telesciences, terence's, tolerances, utterances, variances
Counterbalances sounds like:
counterbalance, countervailing