Just a note of caution, the OP mentioned "Kilbarchan (Linwood)".
Originally Linwood was part of Kilbarchan Parish even though they are 3 miles apart so the Beatties of Kilbarchan (Linwood) may not be necessarily to the Beatties from Kilbarchan.
At the time being discussed, records were compiled on the basis of the parish. Linwood is
in the parish of Kilbarchan. Note that all the birth/baptism records of the family are recorded in the parish/Registration District of Kilbarchan.
The fact that the town/village/whatever of Linwood may not see itself as part of the town/village/whatever of Kilbarchan in the 21st century is irrelevant in the context of this thread.
In the 1861 census the family being discussed here are the only Beatties in Kilbarchan. Not only that, but the 1861 census is the only one in which there is a family of Beatties in the parish of Kilbarchan. (There's a 23-year-old Isabella Beatie in 1891 and a 24-year-old Grace Beatie in 1911.)
Therefore there
are no other 'Beatties of Kilbarchan' in the 19th century to whom this family might or might not be related.
One might take issue with the phrase 'Beatties
of Kilbarchan' because in older Scottish records the word 'of' specifically implies that the person so described is a member of the family who own the place to which (s)he is linked.
A tenant is normally described as 'in' a place, and a temporary resident is 'at'.
