How do I handle the moral weight of having authority over people?

You hold power over people who have lost their freedom, and it unsettles you. That unease is not a problem to solve. It is your conscience doing its job. The day that weight stops bothering you is the day to worry, because that is when authority curdles into something harder and crueler. Many would take a role like yours and never feel a thing, or would enjoy the power. You feel its gravity instead. That means you are the kind of person who should hold it, precisely because you take seriously what it means to have another human being in your charge. The discomfort is the mark of someone still treating them as people. So let the weight stay, and let it guide you rather than crush you. Ask, in the hard moments, what the humane and firm thing is at once, and do that. Keep the unease close as a compass, not a wound. The role will always sit heavy. In your hands, that heaviness is exactly what keeps it decent.