Because moving air pushes on them — the wind exerts a force on every surface it meets.
A leaf lying on the ground has a large surface for its very small weight. When wind blows across it, the air pushes on that surface, and even a modest push is enough to lift the leaf and carry it along. A tree is far heavier, but its leaves and branches present a very large area to the wind, so the total force on the crown becomes large enough to bend the trunk.