Enjoy seeing the new baby for I know most girls like to see & hold the very new ones. Remember, they do say it is catching though --
So what 'catching through' means here?
"It is catching" means that something is contagious. In this case it means, I think, that some people will want to do what they see others doing. Here, it seems to refer especially to children, who tend to imitate what they see adults (and sometimes other children) do.