If we do not balance compassion with equanimity, compassion can easily fall into grief. Wishing for some sort of power to end that person's suffering, when perhaps we do not have the power. Or wishing for the ending of Dukkha in the world and that somehow we have the power, but we do not have that power to end Dukkha in the world. Balancing compassion with equanimity is balancing the caring with the understanding that there are many things beyond our power to control. And so it strengthens compassion so that we can feel with, but not suffer with.
Equanimity is a certain acceptance of things as they are, without preferences, without aversion, without desire, seeing things clearly. It is backed up with a type of wisdom that understands things are impermanent, and that we don't have the power to change impermanent things to be permanent, nor to end the suffering of others if they are not accepting the law of impermanence. That we don't have the power to make everything pleasant for people if their suffering is arising from not accepting that Dukkha exists. And that we do not have the power to make everything theirs if their Dukkha is arising from a non-acceptance that things are not theirs. It's also an understanding that we can only give suggestions but everybody must end the Dukkha within themselves, that we don't have the power to end others' suffering.
So it's important to balance our compassion with equanimity. Then our compassion has a strength, and we are not overwhelmed by the suffering of others, caring too much.