my son is now 15 months, he also asks me to carry him most of the time.
outdoor: he would ask me to carry him if he feels nervous of a strange place, strange people, or he feels tired.
indoor: he would ask me to carry him if he feels tired, sleepy, hungry, thirsty or cannot win his brother, or if I carry his brother, or when he wants me to play with him.
sleep: he would sleep by himself if his father stays with him, but if I am the one who stay with him, he won't sleep unless I carry him
I don't know why, I just assume he loves me and feels good when I carry him. Because he doesn't want me to carry him when he is playing happily.
His brother was like this before, and sometimes even now. But he has no problem going to school or playgroup, no crying.
So I just assume they are all normal, and they just love me so much that they miss me sometimes, and want me to carry them.