My Lexi and Riley are very much this way. Lexi is attached to me all the time if she sleeps she is touching me so she knows if I move she will not be left behind.
Lily sometimes but not near as much I wonder if it is because she was born here and just very comfortable. And Riley attaches to anyone who is sitting still. Otherwise he follows every where also. They just love being around people. Enjoy it don't fight it