You are absolutely right, Nagi. "Weeping effigies" does refer to the iconography of the Roman Catholic church. This song is written by the Pogues, and they are talking about Ireland. Throughout the nineteenth and early twentieth century, millions of Irish people were forced to leave their country because of poverty and even starvation - particularly during the Great Famine of 1845-52. Even though life in their home country was so miserable that they had to emigrate, wherever Irish people are in the world they still celebrate Ireland. The song emphasises this paradox.

This song is all about people coming to the western world, and at times, it didn't turn out to be what they had hoped. They are in a land that makes them refugees, they are presented by the priests with empty plates, and they see sculptures (effigies) of people weeping and having guilt, of possibly leaving their Mother country. But yet they still celebrate and dance. Priests are of the Catholic religion and at that time the church would knock on everyone's doors and collect taxes. The people had the fear of having to pay taxes, or the fear of not having the money to pay taxes. I have not seen many sculptures or pictures, however, some of them were sad. The saying; "the grass is greener on the other side of the fence," doesn't always hold true. Things are not always as they appear:-) This may be where the guilt and weeping comes from. Things are difficult just to survive. Different country, possibly different language, etc. Hope this helps!