Have been having a rake about in the Caledonian Mercury, which I can access via the National Library of Scotland.
Jarvey John in Balbairdy aged 78 years Palsey died Feby 7th 1797. [Bathgate Parish Register]
Sequestrations etc. 1801. July 27. John Baillie, vintner at Broxburn. Creditors to meet in the house of John Jarvey, vintner in Bathgate, on the 1st August next, at 12 o'clock noon, to name an interim factor; and again, at same place and hour, on the 19th August next, to chuse a trustee. [Caledonian Mercury, 5 August 1801]
Lost. Dropt on Tuesday, the Three following Bills: £67:9:7, due 15th and 18th March 1805, accepted by Armstrong and Co Edinburgh; £26:11:0, due 7th and 10th March 1805, accepted by Wm Pender, Airdrie; £21, due 3d and 6th January 1805, accepted by John Jarvey, Bathgate. As payment of the above Bills is Stopped, they can be of no use to any person except the drawer. For the above bills a handsome Reward will be given, by applying at the Caledonian Mercury Office. [Caledonian Mercury, 27 December 1804]
Died. Upon the 14th Ult Mr George Jarvey, vintner in Bathgate, aged 80 years. Mr Jarvey contributed largely towards the improvement of Bathgate, his native soil, and afforded the inhabitants the pleasure of walking in a beautiful garden, scarcely to be equalled in a country village. It will be a circumstance gratifying to his friends, that as he lived respected, so he died much regretted by his numerous acquaintances. [Caledonian Mercury, 8 March 1806]
We hear from Bathgate, that on the evening of Tuesday the 11th curt (being old New Year's Day, which the masters of servants in country towns, rather improperly allow them to indulge in noctural inebriations), a number of young lads, apprentices of mechanics in that place, broke into the gardens of the peaceful inhabitants, and wantonly destroyed the fruit trees, and others within them, particularly into the beautiful and delightful garden, the property of Mr Jarvey, vintner, in which they broke down and destroyed some very fine statues, which ornament it. From the vigorous and cautious steps adopted by Mr Jarvey, most of the delinquents have been apprehended and committed to prison by the Justices of the Peace. [Caledonian Mercury, 16 January 1808]
Scots Bankrupts. William Fleming, Vintner, Bathgate. Creditors meet in Jarvey's inmm 15th June, 12 oclock, to name a factor; same place and hour, 15th July, to elect a trustee. [Caledonian Mercury, 11 June 1808]
To the Creditors of John Jarvey, late Vintner, Bathgate. In the process of multiple-poinding, depending on the Supreme Court, before Lord Meadowbank, Ordinary (Mr Rose, clerk) at the instance of James Corbet, surgeon, royal navy, against the creditors of said John Jarvey, his Lordhsip, by interlocutor of 9th July 1811, appointed John Gibson, writer to the signet, to be common agent for carrying on the process; and of new ordanied the creditors to produce their interests against the first box day in the present vacation, with certification, and appointed intimation to be made thereof; of which notice is hereby given to all concerned. [Caledonian Mercury, 8 August 1811]
I think, if I put all this together, that John Jarvey, vintner, Bathgate, was the son of George Jarvey, vintner, Bathgate, who was born about 1715 and died in 1806. As John Jarvey in Balbardie died in 1797, he cannot be the same person as the John Jarvey, vintner, in whose premises creditors' meetings were held in 1801 and 1808, and who was himself sequestrated in 1811.
Therefore George Jarvey senior could be a brother of John Jarvey in Balbardie, and yes, he had at least one son so may have had others, for example your George junior born about 1766.