just reassure him (over and over again if necessary) that when you do the right thing (like hugging your mom or doing a random act of kindness) there is no need for an apology. but there is a reason to be acknowledge. try to preempt his apologies by constantly praising him for some of the good things he is doing. if he happens to do a non-so-good thing you may want to just let it slide for a while praise goes a long long way in modifying behavior. even if that behavior is already pretty-good to begin with.
my 12 year old is constantly saying he is sorry for everything? . we have talked to him about it and he says nothing is wrong. we think it may be due to his older brother being a difficult child (he have adhd and is diagnosed rapid cycling bi-polar). an example is he gives his mother a hug and then for no reason apologizes. we offer to take him to a psychologist but he take it as a threat even after we explain that it would give him a safe place to talk if he feels he can't talk to us. is it just a self esteem issue. just need some advice.