The Collaborative International Dictionary
Thirlage \Thirl"age\, n. [Cf. Thrall.] (Scots Law)
The right which the owner of a mill possesses, by contract or
law, to compel the tenants of a certain district, or of his
sucken, to bring all their grain to his mill for grinding.
--Erskine.
Wiktionary
n. (context obsolete English) (''Scots'') The right of the owner of a mill to compel tenants to bring all their grain to that mill for milling.
Wikipedia
Thirlage was a feudal servitude (or astriction) under Scots law restricting manorial tenants in the milling of their grain for personal or other uses. Vassals in a feudal barony were thirled to their local mill owned by the feudal superior. People so thirled were called suckeners and were obliged to pay customary dues for use of the mill and help maintain it.