Culpeper places willow under the Moon, and gives two grounds: the tree's affinity for water, which is the Moon's element in the elemental scheme, and its cooling action. In his system that is a coherent argument, and it is the argument, not an observation.
The wider symbolic load on the willow is older than the herbal and largely independent of it. The tree is the standing emblem of grief and of forsaken love in English usage, the green willow garland worn by the jilted, Desdemona's willow song in Othello, the willow of the Psalm 137 exile, though the tree in that verse is more probably a poplar. Its weeping habit is the obvious source, and the weeping form most familiar in Europe, Salix babylonica, is in fact an East Asian species carried west along the trade routes and given a Babylonian name by Linnaeus on the strength of the Psalm. The name is a mistake preserved in the botanical record.
Willow is also genuinely useful in ways that have nothing to do with symbolism. It coppices readily, roots from a cut stake pushed into wet ground, and yields the withies for basketry, hurdles and creels; it is planted to stabilise riverbanks; and it is the timber of cricket bats, from a particular cultivated variety. The association with water-divining rods is real as folk practice and the practice does not work under controlled test, which has been examined repeatedly.
The ease of rooting deserves emphasis, because it probably underlies the symbolism rather than the other way round. A willow stake driven into wet ground will grow. Cut a willow hard and it responds by growing more vigorously. A tree that cannot be killed by cutting, and that reproduces from its own severed parts, is a natural emblem of grief that persists and of life continuing after loss: and pollarded willows, cut back repeatedly to the same knuckled head, are among the most characteristic and most obviously artificial features of the northern European landscape.