I agree that THINGS THAT ARE BALANCED is the better phrasing. "Balance" is somewhat of an active property -- people balance, but things are balanced.
Your acceptable clues are justice's scales ("scales of justice" I would accept, since it is an actual name like "mother of pearl"), a gymnastics beam walker, a checkbook, "the books", your newly mounted tires, yin and yang, etc.
That turn of phrase could allow "a gymnast's beam".
Your do-not-accept list would be your credit card transfer, your equilibrium, your remaining funds, terms that describe the act of balancing ("weighing" etc.).
The keyword would, of course, be BALANCE.