Moate, Athlone Poor Law Union (also Registration District for births, marriages & deaths), County Westmeath. Moate is split between 2 civil parishes, Kilcleagh and Kilmanaghan, both in Clonlonan barony.
(Information from Placename Search on SWilson.info
https://swilson.info/index.php)
Griffiths Valuation
www.askaboutireland.ie/griffith-valuation/Search for entries for Weir surname in Westmeath. 22 results, some as occupier, some as immediate lessor including:.
Kilmanaghan civil parish, Clononan barony, Athlone Union
John Weir, Newton townland, occupier house & yard.
Newton townland with 7 individual holdings, follows "Town of Moate (part of) detached portion" in townland of Legen in the parish of Kilmanaghan.
The name John Weir appears in other entries in the county.
SWilson.info is a website which is useful for finding places, identifying religious and civil parishes, registration districts etc. Another function is surname distribution.
https://www.swilson.info/index.phpTo find the name of registration districts in a county: Select Registration District Map Browse and then select county. All registration districts in Offaly cross county borders as do most of those in Co. Westmeath.
When you know likely registration districts you can search for deaths of the parents, assuming they remained in Westmeath and that they survived until 1864. BMD registers on Irish Genealogy.ie are organised by Superintendent Registrar's District which were based on Poor Law Union districts.
https://www.irishgenealogy.ie/enBirth, marriage and death registrations from 1854 + non-Catholic marriages from 1845.