David was born 1811 (if died aged 34).
5 Sep 1831, David Wood, Wood Turner married Sarah Henshall
In 1841, there was a David Wood (Carder) who married Sarah Cotterill 27 Mar 1831 with family at London Road, Manchester. This is another family, still alive in 1851.
Only Manchester death record for David Wood after 1837 is in Q4 1845, aged 34, but Sarah was a widow in August 1845. There are no other matching records, so David must have been terminally Ill, the death was registered late, and Sarah remarried immediately after. They had Matthew in 1845 so he must have only recently died.