I have in William & Catherine family 5 sibling's.
2 Williams, 1 died an infant. 1 Catherine and 2 Edwards again 1 died an infant. I haven't found a John.
There may be a connection to an Alexander, perhaps William's brother. Alex Bailey m. Mary Robinson had a son Alexander b. 19 FEB 1764, d. 28 JAN 1765, could this be William's brother and parents?
It would appear that Edward is a dominant family male name.