My impression is JA uses chapter 2 to tell Mr Weston's family background and how being Captain Weston has affected his life.
Mr Weston was of respectable local family and it satisfied his active, cheerful mind to enter the militia.
Captain Weston was 'a great favourite and 'chances of military life' led him to meet Miss Churchill. During their 3 years of marriage he remained in the militia as JA refers to him as Captain Weston. They lived 'beyond their income' on the death of his wife he quitted the militia to engage in trade with his brothers in London; While Frank is given to the care of the Churchills.
By the opening of 'Emma', Mr Weston has made his fortune and purchased the small estate of Randalls. As he hasn't been a militia officer for some time, apparently he is known as Mr Weston.