I understand a stint is placed to allow the kidney stone to pass. But why would they wait 3 weeks after the stint is placed to laser the stone?

Kidney stones. The stent is passed more to insure good urine flow (avoid blockage) than to pass the stone. The reason they wait is to allow the inflammation caused by the stone, when it's under a lot of pressure, to settle down. There are fewer complications with definitive treatment when the inflammation is resolved.