Yes your experience is limited. Birth rates rise when children are an income producing asset. The shift from rural to urban populations dramatically lowers the birthrate since normally children are only an expense in a urban environment. However in societies that pay out money per child there is an incentive to have more children and the birth rates for the poorest tend to rise. This phenomena has been documented around the world and has nothing to do with your views on religion.
My views on religion? Um? Both my parents grew up in families with 9+ children because all of my grandparents thought birth control was a sin. That's my experiences. That's in an urban setting. All their large family neighbors did it for religious reasons too. I don't personally know a single large family that isn't doing it for religious purposes. There are also some large families who are doing it for religion in the media such as The Duggars as well as some public movements for large families such as Quiverfull.
Thats nice. The data disagrees with you. Just google up urbanization birthrate for many papers on the topic.
Isn't the marginal support per child something absurdly trivial after the first few?