Welcome to the Forum.
Many thanks for unravelling this mystery. If I have it right, both Jacob and Matthew jnr were Alderman.
Jackson has Matthew West (who you have indentified as MW sen.) as the son of Jacob West of Kildare and apprenticed to John West in 1762 (making him around 15 years of age, which would just the right age). John West is noted as being the son of Jacob West, farmer, of Queensborough, County Kildare. Could John West be Matthew's (sen.) elder brother? He died in the same year as Matthew, 1806.
Also can you throw any light on George West, goldsmith, working in Dublin 1792-1828.
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