Ah, that makes more sense - and interesting about the rush to enrol at election time!
Unfortunately I have little else. Most of the Balnes seem to originate (or at least congregate in the 17th C) around Snaith. Balne was a parish of Snaith, now a separate village or town.
I am working from a son John (or possibly Jonathan - being referred to as Jno.) Balne who is the son of the Bristol John, who seems to have moved (collecting wife and kids along the way) to Poole and then to Fordingbridge in Hampshire.
These seem to be death records for John the son and his wife Mary:
John Balne who dies in Poole in 1842:
https://familysearch.org/ark:/61903/1:1:2JQM-WQ8 - seems likely to be this one.
A Mary Balne who dies in Poole in 1838:
https://familysearch.org/ark:/61903/1:1:2NRQ-PJJAnd I'm thinking that his is probably the burial record for John the father:
buried in Bristol on 13 June 1766:
https://familysearch.org/ark:/61903/1:1:J86T-6M2(Quite likely unrelated, but the earliest Balne I could find in Somerset is Richard Balne, who is present for the christening of daughter Elyzabeth in 1610:
https://familysearch.org/ark:/61903/1:1:J31W-P9W and dies in 1629:https://familysearch.org/ark:/61903/1:1:JDQ1-GZP)
As for the pronunciation and spelling: I believe that the village in Yorkshire is pronounced "Bawn", but that my closer ancestors pronounced it "Ballin" (west country influence?). Hence quite possible that some surnames were written as Bawn or Baun... but anyway, the one who ended up in Hampshire via Dorset spelt his name Balne and passed it down spelt thus.
I don't know anything about their occupations other than a son of John Jr was apparently a carpenter... The two sons' names were John Humphrey Pinhorn B and Vincent George Boucher B - each taking a name from mother and grandmother, so that fits.