May drowns herself by weighing herself down with a stone. Since the terrible death of her twin, she has had a difficult time dealing with the sorrows of the world. She had strategies to deal with her tendency to take on the world's sadness, for example, singing, and placing "messages" at her Wailing Wall. But when Zeke is imprisoned, it finally becomes too much for her. Many readers guess that she will kill herself before the event actually occurs. You might want to look through the book to see what kinds of foreshadowing the author creates. She is so tender-heartened, it seems impossible that she can survive the turmoil of the South in the Sixties.
Interestingly, a famous author, Virginia Wolfe, who probably suffered from bi-polar disorder, did commit suicide in a similar way. She weighed her pockets down with stones and walked into the river. This event was a rather famous literary suicide, and it seems likely that Sue Monk Kidd was thinking about Wolfe when she wrote about May's suicide.