I tend to wax my string lightly after every lengthy shooting session or after I my bow has been outside in very warm and/or dusty conditions. Can you overwax? Yes. When the string has too much wax in it the string will have build-up and can collect more dirt than normal. After you apply your wax, rub the wax into the string thoroughly with a small piece of leather. Rotate the leather often as it will collect the dirt from your string into it. You want to rub the wax in good so that you feel a little heat. This very small amount of heat helps the wax flow into all of the fibers of the string. If you use the leather patch as I described, it is pretty unlikely you will have left too much wax on the string. However, some folks will also take a short piece of floss or serving material, make one loop around the string and then slide this up and down the entire non-served and loop portions of the bowstring after the wax was rubbed into it. This removes any excess wax and build-up. Personally, I haven't needed to do this when I use the leather patch.
CAUTION: DO NOT BE LAZY AND USE A HAIRDRYER TO MELT THE WAX INTO YOUR STRING! The heat produced by them could damage the string without you even knowing it.