Is it normal for women to be "big babies " ?

I think the person calling someone a "big baby" is the baby.

Because they think its cute -.-

Of course immaturity and neediness are not exclusively male traits, but I think for some reason this expression is only used for men. As a guess I'd say that this is because (most) men don't grow out of liking breasts and some enjoy being mothered, probably more than women.

Men are more childish than women. But women are too blind to see it, well... a good variety of them.

I suppose it comes down to gender stereotyping. As Emily said, anyone can be a "big baby".
Though I think women are probably more likely to be big babies in the eyes of men due to us being more hormonal more often than them. It's also considered feminine to have a vulnerable, emotional side. Then again, they say that men are big babies probably because they are just as vulnerable and emotional but they try to hide it more to live up to the 'manly' stereotype.
I think that teenagers in particular are likely to be "big babies" what with adolescent hormones just beginning to affect behaviour.

They most certainly are.

immaturity is not related to gender.

Anyone cam be a big baby

Yep.