Shelia, you asked me to comment on your other thread on the England board. I'll comment on this thread so that everything is in one place
You seem to be chopping and changing so far as his birth date is concerned. Originally you said it was 1838, now you’re saying it was 1840. Where does 1840 come from? The 1870 census perhaps? In the 1880 US census Aaron gives his age as 42, yet in 1900 he gives a date of Nov 1836. So there are no two censuses that give a consistent date, which means that none of the three ages can be regarded as reliable.
The Aaron, presumed son of Lucy, in 1841 in Gt Waltham was aged 1 – the census date was 6 June 1841 so assuming age 1 is accurate he could have been born between 7 June 1839 and 6 June 1840, and I’m confident that the birth registration in the Dec quarter 1839 is the same Aaron, but you need the birth certificate to prove it.
However your real need is to prove that the Aaron Stock in Missouri is the Aaron Stock son of George and Lucy. Do you have Aaron’s NY marriage entry? Does it name his father/parents? If so you’re home and dry, so long as it's George and Lucy.
The burial entry of an adult would not normally detail parents – it might add “farmer” or “labourer” and an age but that’s all unless you’re very lucky. The civil death certificate will not give parents, just the name of the informant, which, if you’re lucky again, might be his wife, who we assume to be Lucy.