Just called the board of education to ask them if their are any regulations or guidelines regarding this, but according to them their aren't any in the city of Amagasaki.
Thing you can do is talk to the school, and the homeroom teacher regarding when and when not to leave the books at home/school.
Still I think it is strange, that kids need to carry a bag that heavy... or is it just me.
How about everyone else, do you remember if you had a heavy bag when you went to elementary school?