The Weir takes place in a pub in an Irish village near Sligo. Jim is the bartender of Brendan's pub, which is located within Brendan's farmhouse.

The play opens with Jim and Brendan swapping stories with Jack, a regular customer and mechanic who is the oldest of the three. The men have lived in the village all their lives, so they are keenly aware of the details of each others' lives. All three enjoy telling ghost stories while they are drinking. Some of the supernatural tales are about occurrences in the village, while others expand on traditional stories their grandparents loved to tell them as children.

They also discuss an upcoming change: an outsider has rented a house via an agent named Finbar, who is a formerly-local man. They comment that, as a married man, he seems to be spending too much time with the renter, who is female. Soon, Finbar comes in with this new renter, Valerie, who has moved to the area from Dublin (where Finbar now lives).

Continuing with their trajectory of ghostly tales, they tell Valerie that there is a "faery road" running underneath her house. While they show signs of rivalry for her attention, their attitudes are rather skeptical of her presence, both as a woman (and therefore out-of-place in the pub) and as an outsider. Valerie does not seem dissuaded by their tone, however; she has obviously made a difficult decision in uprooting herself and wants to establish her place of in the town.

It turns out that a personal tragedy had made her want the change of venue: she lost her young daughter to drowning. As the mood turns serious, Jack shares his own (apparently true) story, rather than another ghost tale. He recounts the loss of a former lover and how the resulting loneliness has effected his life. Their attitude turns toward acceptance, as it seems Valerie may fit in with their melancholy town.