I think it's the other way around. I don't think there is any prejudice against small families. Maybe in some more conservative areas of the country but that is a shrinking amount. Large families are now seen as very poor, uneducated or very religious. Many times they are mocked. Having a small family or some cases, no children in a marriage, is increasingly seen as responsible.
There is a growing chasm in this country anyway, between those with children and those without. Voting patterns reflect this phenomenon. I don't remember seeing or hearing anything like it when I was growing up. It's appears especially acute among women. I can't tell you how many times I've heard disparaging remarks by childless women towards women with children. And vice versa. Although they vitriol seems to come from those without kids. The men pile on too. I don't hold a grudge against either group. I don't get it. You have to respect other people's choices.
Great question and food for thought.