Hello Brigyn,
Thank you for making me think again about that 'Archibald'. If Hugh Fraser had followed traditional naming patterns, the first son should have been William for his father but that was used for the second son. When I first starting researching, I tried to make sense of it and didn't find an Archibald in the family and so thought that it was part of the pattern of increased frequency of the name linked to Archibald Fraser who assumed the Chiefship of Clan Fraser in 1782. Archibald died 8 December 1815, at the age of 79. That may be the explanation but...
There are a two Archibalds that are born in Kirkhill and one in Kilmorack with father William that I should look at:
Archibald Fraser birth: 04 Aug 1774 christening: 08 Aug 1774 KIRKHILL,?INVERNESS,?SCOTLAND
parents: Hugh Fraser,? Anne Fraser
Archibald Fraser birth: 16 Jun 1783 christening: 17 Jun 1783 KIRKHILL,?INVERNESS,?SCOTLAND
parents: Finlay Fraser,? Katharine Fraser
Archibald Fraser christening: 21 Jul 1788 KILMORACK,?INVERNESS,?SCOTLAND parents: William Fraser
[I had wondered if I hadn't missed siblings for Hugh besides Jean born 22 Sep 1776 Wester Moniack as the gap of 7 years stood out. If there were, since there aren't any records with Janet Stephen (or Steven) they were probably just recorded with William's name. I was rather discouraged since there are dozens and dozens in Invernesshire (even if limit to Kirkhill, Kiltarlity and Kilmorack).
Regarding the 1861 census, I transcribed it years ago at the General Registrar's office in Edinburgh so hadn't looked again for it:
Frederick Fraser, head, mar 46, farmer of 30 acres, b. Kirkhill
Janet, wife, mar, 42, farmer's wife, b. Duthil
Ann, dau, unm, 19, farmer's dau, b. Kiltarlity
John, son, unm, 16, farmer's son, b. Kiltarlity
Hugh, son, unm, 14, scholar, b. Kiltarlity
Robert, son, unm, 3, b. Kiltarlity
William, son, unm, 1 b. Kiltarlity
Jane Fraser, serv, unm, b. Kirkhill
Hugh Fraser, father, mar, 78, former school master, b. Kirkhill
The description of Hugh Fraser as a former school master may be an exaggeration as in other documents he's listed as a wright. I do know that he was a poet in gaelic known as Huisdean a Craggen and one of his poems was included in an article by Hugh Barron in the Transactions of the Gaelic Society of Inverness. The poem was a image-rich rant against his landlord who cleared him off of his land.
Thanks for the ideas and questions which make me think!
All the best,
Jessie