Although they had more children, I have only been able to find one baptism: James Tweedie in 1833.
There is a baptism of Ann Blyth Tweedie, daughter of James Tweedie and Isabella Ross, in Edinburgh on 7 August 1828.
What other children did they have, and how do you know about them? Have you found the family in a census?
the family lived 'at the Ness' (if I am reading it correctly) but I am not sure what this means. Is it another name for nearby Alness? Or does it mean that they live close to the water?
A ness is a headland, but if James was baptised in the parish of Rosskeen and the parents' residence is just 'the Ness', not 'the ness in the parish of xxx', then the place you are looking for is in the parish of Rosskeen, or very close to its boundary.
The boundary between the parish of Rosskeen and the parish of Alness follows the Alness River, so the larger part of the town of Alness, east of the river, is actually in the parish of Rosskeen (very confusing!). So I think it is possible that 'the Ness' in this context does indeed mean Alness. See
https://maps.nls.uk/geo/explore/#zoom=15&lat=57.69958&lon=-4.26037&layers=5&b=1 (you may need to zoom in).
BTW Rosskeen and Alness are not on the Black Isle; they are on the opposite (northern) shore of the Cromarty Firth.
You can read about both parishes at
https://stataccscot.edina.ac.uk/static/statacc/dist/county/Ross%20and%20Cromarty