Closing the line might be a bad idea, the pressure that builds up inside could cause the top to blow off or something.
I've always left mine running 24/7 without any problems at all, and i use 2 bottles on the one 12G tank.
Have a look at the fish when you wake up, are they gasping for air? If not, dont worry. If they are, perhaps run an airstone through the night so that the CO2 will be released by the surface aggitation