We have, in the 1841 census, a family in Gt. Waltham headed by Lucy Stock (born 1806) - a Farmer - together with children George (b 1835), Peter (b 1836), Moses (b 1837) and Aaron (b 1840). Although the 1841 census doesn't state marital status, I can only assume that she is a widow. Also in the same household is a 60 year old Mary Stock (Grandparent?).
Aaron's age indicates that George must have died towards 1841 and I can see a burial record for George Stock, age 44, in Great Waltham on 13th Feb 1840. There is also an official Death Registration in Chelmsford (which covers Gt Waltham area).
My records show the same family (minus Aaron) still in Great Waltham in 1851. I had tentatively assumed he had died. An Aaron Stock did in fact die in Stepney, London 1843, the only death registration for an Aaron Stock between 1841 and 1851.
It is not inconceivable [I had thought] that he was taken down to London for medical treatment and died there. An alternative may well be that he went to USA, but I cannot think of circumstances where a (less than) 10 year old would be sent without the main family going with him. But who knows?
It would be possible to dig out the post-1851 'happenings' for the rest of the family (as far as my records show) but I don't know how much of this you might already have.
As to pre-1841, I can find no marriage record of George Stock and Lucy. I guess they might have married around 1830 - 1835, and Parish Records had tended to dry up by around 1820. However, I can trace a baptism record for George Stock on 8th Dec 1794, Great Waltham, son of William Stock and Mary Boltwood (assumed to be the Mary surviving to the 1841 census). I cannot find such a baptism record for Lucy Poole.
If I have the right baptism record for George, then it seems he was the first of 7 children, with sisters Sarah, Mary, and Rosanna, and brothers John, John and James - some of who presumably survived.
Census data does not show any proliferation of "Poole" in Great Waltham, but if you wanted definitively to confirm that Lucy Poole is Aaron's mother, then this would be on his birth certificate - registered Chelmsford 1839 Q4, Vol 12 Page 40, obtainable from the Register Office.