Not an equilibrium of force, but at least some states do require that the defendant relying on self-defense used no more force than was reasonably necessary to defend against the particular threat posed. Take California for example:
As the jury was instructed on the assault count, a defendant acts in lawful self-defense if “one, the defendant reasonably believed that he was in imminent danger of suffering bodily injury ... or was in imminent danger of being touched unlawfully; two, the defendant reasonably believed that the immediate use of force was necessary to defend against that danger; and three, the defendant used no more force than was reasonably necessary to defend himself against that danger.”
People v. Clark, 201 Cal. App. 4th 235, 250, 136 Cal. Rptr. 3d 10, 22 (2011)(bolding added).
Such a requirement is a good one. IMO it would be unjustified, for example, for Amy to shoot and kill Blake in response to a threat by Blake to throw a cotton ball at her, as presumably a much lesser degree of force would be needed to deal with that threat. If I were on the jury in her murder trial, I would likely reject her self-defense claim of killing Blake. She’d have to make a really amazing case that the threat she faced justified it, and that would take more than just a toss of an ordinary cotton ball.