Why do RC circuit voltages decay *slowly* rather than instantly?
OUT is simply a label so that the simulator can assign a voltage at that point. It is not part of a charging/discharging circuit.

The basic rule of capacitor charging is that you cannot instantly change the voltage across a capacitor (unlike a resistor). The capacitor in your circuit starts off with no energy and has 0V across it. So OUT will show as 0V. On the rising edge of the input the full voltage of the pulse appears across the 100R resistor. If the step voltage is V then the initial (charging) current will be V/100 amps. As the energy stored in the capacitor increases the voltage across it will increase (Vc). This reduces the size of the current  (V - Vc)/100 amps. It is this increase in capacitor voltage that produces the characteristic exponential charging curve.



It will take ONE TIME CONSTANT (C x R) to reach about 67% of the final value. 

When the input pulse returns to 0V the capacitor will start to discharge through the 100R resistor.