What is believed to be the oldest brass weathervane in England is still atop a 14th century parish church in Etchingham. (Update: it now seems to have been moved into the church) The Etchingham arms are pierced into the vane, and unlike later vanes the banner is not balanced by an arrow on the opposite side of the pole. As far as I can tell from the tiny images, this is also true of the banner weathervanes in the Tres Riches Heures.
Several images from 1380-1415 appear to show weathervanes atop tents, and they are explicitly mentioned in the 1496 Accounts of the Lord High Treasurer of Scotland, where they are made from dowbill platis, which in other references are described as white iron or tinplate. They were painted by the same painter who painted the king's coat armor. The 1547 inventory of Henry VIII's possessions mentions, associated with his tents, 66 vanes of ironwork "painted and guilted with the the kings Armes and badges".
A vane associated with the early 17th century pavilion in Basel is dated on the vane to both 1591 and 1736. This relatively late vane is also unbalanced.