The OED has examples of this word from the sixteenth century, in my sense of ‘waterproof’, but in coal-mining it was used occasionally of a pit or gallery that could not be worked because it was flooded.
A husbandry practice which involved flooding meadows early in spring to promote the growth of the grass (CA45). A weir had to be built across the brook so that water could be run off and distributed via channels.
The suffix ‘gate’ is important in this case for it could have two meanings. In the sense of ‘barrier’ or ‘door’, it was a contrivance that had to be opened if water was to pass through, in the sense of ‘road’, it referred to a water course or channel.
At the end of the coppice cycle, when the trees were felled, a certain number were allowed to remain, in order to provide a later crop of timber trees. These were called standards, or more commonly in Yorkshire ‘wavers’.
A weir is now most commonly thought of as a dam, placed across a river to restrict and control its flow rather than stop it altogether. Formerly, it had several meanings connected with river defences and these can be linked with bridges and the strengthening of river banks. Most commonly, it referred to an embankment reinforced by piles.
Weirs were initially reinforcements to an existing river bank, formed of piles, but the need to heighten and strengthen the defences resulted in the building of stone walls, often but not always linked to bridges. The verb 'to weir’ was used in such contexts.