In the 1851 census the address for James Cowie and family is "Backhill Of Overhill", New Deer.
So it is. In which case it's not the Backhill in the parish of New Pitsligo that I found earlier.
In 1851 it's in Enumeration District no 2 of New Deer, along with Affath, Nether Affath, Weetingshill, Backhill (of) Weetingshill, Auchouch, Meikle Auchouch, Sandbridge, Wellhowe, Doghillock, Brownhill, Henscroft on Brownhill, Skelliebogs, Overhill, Backhill of Overhill, and Whitehill.
In 1861 it's in Enumeration District No 7 of New Pitsligo, along with Broomhill, Cranhill, Ironside, Upper Ironside, Overhill, Smithy, Dog Hillock and Back Hill, all of which are in the ecclesiastical parish of New Deer, and Craigculter, Red House, Achnary, Lambhill and Whitehill, all of which are in the ecclesiastical parish of Strichen.
The really striking thing about these lists is how few of the names are the same in both censuses, apart from Doghillock. Look at this map
https://maps.nls.uk/geo/explore/#zoom=15.0&lat=57.56539&lon=-2.18845&layers=5&b=1&marker=57.57130,-2.26079 which shows Doghillock over to the right. Above and to the left is Broomhill, and left again is Overhill, printed vertically up what is the edge of a map sheet. Left again is Brownhill. Down from Brownhill is Ironside, including Backhill of Ironside. So is Back Hill the same as Backhill of Overhill in 1851 and Backhill of Ironside in 1861?
This is it on a modern map
https://www.geograph.org.uk/gridref/NJ8751 - click on the map and move it about to see Doghillock, Overhill etc.
Some information from the Ordance Survey
https://scotlandsplaces.gov.uk/digital-volumes/ordnance-survey-name-books/aberdeenshire-os-name-books-1865-1871/aberdeenshire-volume-08/49
Unfortunately that is the wrong Backhill - it's in the parish of Belhelvie, which is on the coast well south of the area we're looking at. Here it is on a modern map
https://www.geograph.org.uk/gridref/NJ9318.
There are places called Backhill in 33 different parishes in Aberdeenshire alone, and in at least one parish in ten other counties. And that doesn't include the ones where the name is split to make it Back Hill - there are only 19 parishes with one of those in the whole of Scotland.
This is Little Mill in Ellon where Thurlow Fraser was working at time of 1861 census.
https://scotlandsplaces.gov.uk/digital-volumes/ordnance-survey-name-books/aberdeenshire-os-name-books-1865-1871/aberdeenshire-volume-29/148
See https://www.rootschat.com/forum/index.php?topic=758930.0 for a bit of background.
Did you notice that there's yet another Backhill, Backhill of Ardlethen, just up and left from Littlemill of Esslemont?