Do you like how curious you are? Is it a blessing or a curse for you?

I think it goes back to caring and not caring and I care too much

If we are talking about questioning someone actions, inactions, etc., then it might be more a suspicion (or gut feeling) that something is awry. I of course don't know if it's this type of "caring' you are referencing, but... if it is, there is nothing wrong with questioning suspicious/unusual behaviors. Unless of course, one carries it too far, it can wreck a good relationship.