Equiponderancy is a term used in archaic English to refer to the state of being equal in weight or importance.

The equiponderance of the two objects was evident when they were placed on the scale.

The judge equiponderated the evidence before making a decision.

She is equiponderating the options before making a decision.

It is important to equiponderate the pros and cons before making a decision.

He equiponderates his options before making a decision.

The two boxes on the scale were equiponderant.

The two boxes on the scale were equiponderous.

Equiponderation is the act of balancing or equalizing weights.