Here's that 1940 census, for the record. Hard to find "your" William Stewart as there are many of that name and age in those locations (South Dakota, Kansas, Missouri). Do you have more clues? Is little Williams's middle name Lee? What does the L stand for in Dorothy L Wilson? I am wondering if big William is William Lee Stewart.
Often couples of that era got married in the town where the bride's parents were living (this is still often true). Do you know where Dorthy lived ca 1933?
Kansas City, Wyandotte, Kansas
William Stewart 31 b So Dakota, machine operator(hard to read) feed mill <----
Dorothy L Stewart 23 born Kansas, married 7 years (ca 1933)
Helen M Stewart 5
Donald J Stewart 2
William Le Stewart 11 months old
Residence in 1935: Lesummit, Missouri