Your son, need not pitch every week in the off-season, but he should throw everyday.
At 13, in the off-season I had my son playing on Saturdays and Sundays in two different leagues. But every parent is different.
It is more important that he have a regular daily (light) weight training regimen that he does to strengthen his arm. Running everyday is important, or at least every other day to build stamina and strengthen his legs.
Here is what is recommended by the American Sports Institute for arm usage on players of your son's age group:
http://www.asmi.org/asmiweb/research/youthbaseball.htm