Weaving generally had been a fairly common occupation during the medieval period in Scotland. The skills were taught to apprentices, who may or may not have been related to the master weaver. This remained the normal way of teaching skilled trades right up to the industrial revolution.
In 1587 the Scottish Parliament passed an Act intended to encourage skilled Flemish weavers to move to Scotland, and so develop the local skills base in Scotland. Weavers who moved to Scotland were required to take on Scottish children as apprentices:
"Item, the said craftsmen are obliged by this act to take no apprentices but Scottish boys and maidens of this realm, and before any others, the burgesses’ bairns of Edinburgh to be preferred and accepted upon the conditions following, to wit, to be apprentices by the space of five years and that the said strangers shall teach their apprentices some part of their craft, whereby their labours may be worth their meat and clothing within the space of half a year after their entry; and thereafter the said masters shall instruct them in the whole points of their said craft within the space of five years and shall hide no part thereof from them ..."
To give one example from the late 18th century, the Scottish poet Alexander Douglas was apprenticed to a linen weaver in Fife, when he reached the age of 14. Apprenticeships typically lasted for 6 or 7 years at that time.
A family historian called Adrian Bruce has written a page about linen weaving in 18th century Scotland in relation to one of his ancestors. Although the focus is on Dundee, rather than Forfar, many of the details will be applicable to your case. He notes that:
Linen had become Scotland’s most important export in the latter part of the 1700s, but there were different types of linen and these were made in different areas. Dunfermline, for instance, was the centre of fine work, such as damask tablecloths and napkins. Dundee, on the other hand, specialised in plain and coarse linens, which might be used for such things as sheets or even bags to contain sugar or cotton.
As with most trades, there were three “grades” of weaver – apprentice, journeyman and master. Apprentices were pretty much as we might expect. An apprentice was indentured to a master for a period that was usually about seven years, plus, in Dundee, a further year “for meat and fee”. This last year was regarded as being payment for board and lodging because the apprentice lived with his master for the period of his apprenticeship – indeed, the master was responsible for both the welfare and the morals of his apprentice. Such an apprenticeship might start as early as twelve years of age.