There is proof of the Hamiltons being active in Drumbeg in Ros davies, the TABs 1823-1837 and later Griffiths 1863, see below which suggests he could be part of a Drumbeg Hamilton line. If he was not a Drumbeg native but a Hamilton from Ballywalter was visiting with his wife native for some reason that they are related . the solution would be a church baptism record ie the proof of your notes
Another thought that something happened at Ballywalter and he inherited a farm in Ballywalter already being perhaps related back to a grandfather etc
He would have been about 47 in 1830 with an established family his father speculation a James or more speculation a Brother James
ros davies gives
Miss Margaret HAMILTON Drumbeg wife of Arthur Maxwell Esq.; mentioned in Deeds dated 1721 Registry of Deeds, Dublin Vol 7 p484
Andrew HAMILTON . Drumbeg will dated 9 Aug 1825 IIW # 29256
Samuel HAMILTON . Drumbeg & Annahilt a labourer of Creevy; son of Arthur Hamilton (a weaver) ; married Margaret Kennedy 25 Nov 1853 at Cargycreevy Presbyterian Church, Annahilt; witnesses were William Wilson & John Kennedy PR/CR
Rev. Vesey HAMILTON . Drumbeg curate in Drumbeg ; died 3 Jun 1743 from fever & cough General Evening Post, London 18/6/1743
1823-1837 Tithes Applotment Books based upon the index work of the Irish Genealogy Hub’s listing for each parish in Northern Ireland, The relevant original books are in the
Public Record Office of Northern Ireland (PRONI) Belfast
Hamilton, Andrew-Townland: Drumbeg Year: 1830-Drumbeg-Antrim & Down
Hamilton, Andrew-Townland: Drumbeg Year: 1830-Drumbeg-Down-
Hamilton, James-Townland: Drumbeg Year: 1830-Drumbeg-Antrim & Down
Hamilton, James-Townland: Drumbeg Year: 1830-Drumbeg-Down-
Griffiths valuation pub 1863 arranged by townland in Drumbeg see
http://www.askaboutireland.ie/griffith-valuation/Hamilton Charles Ballyaghlis Drumbeg Down map ref 7
Hamilton James Ballygowan Drumbeg Down map ref 2
Hamilton Arthur Bally Macbrennan Drumbeg Down map ref 20
Hamilton William Cargacroy Drumbeg Down map ref 42
Hamilton Samuel Drumbeg Drumbeg Down map ref 4
Hamilton Mary Drumbeg Drumbeg Down map ref 27, map ref 32, map ref 34
Hamilton James Drumbeg Drumbeg Down map ref 31, map ref 32
Andrew Hamilton (c1820 [81 in 1905 so b~ 1824-d 1905) farmer in 1901 m.~1875 see notein 1911 census
www.census.nationalarchives.ie/pages/1911/Down/Ballywalter/Ballywalter_Town/265659Hamilton Sarah Jane of Sea View House Ballywalter county Down widow died 31 October 1933 Probate Belfast 5 June to Eleanor McMurray Bowden widow. Effects £402 16s. 6d.