Our kids show their immaturity in a lot of ways. But it is more than immaturity. It is lags in learning due to neglect or abuse. When children are in crisis mode they miss stages of development. Think about times when you were in crisis. If someone had tried to teach you something new, asked you to balance the check book, recite a long poem that you know during the time would you have been able to do it? Chances are no because you'd be so focused on just getting through the experience.
One of the ways this lag shows up is in the way our kids look at us. Bear checks in many times with me. If we are church he sits up at the front with the youth but turns back periodically to look at me and see if I am there. When we are home he likes to be alone but wants to check periodically to make sure I am there. All of this is similar to the toddler's typical behavior. They want some independence but check mom's face periodically to make sure things are ok. They toddle off to play but come and check in regularly for some reassurance.
While it may be annoying to have your child demonstrating these behaviors I think it helps if you remember that it really is a stage of life they are making up. Reassurance rather than "Why are you always looking at me like that?" will take you further in healing.
Have a healing day!