Pretty strict
I will say that it is pretty strict, especially from their personalized Terminal 2 at KIX. They have staffs weighing carry-ons at the entrance to security.
I have seen female passengers carrying a roller-on suitcase and a small handbag. I have also seen male passengers with a small lap top case/small backpack and a roller on suitcase. However I have also seen staffs making people consolidating their carry-ons especially if they purchase small items at the airport duty free shops!
So I will say that they are pretty strict! They are polite but pretty strict. I don't blame them as they need to earn $$$ somewhere and you also have more walks and they use stairs for boarding at KIX.
Carfield