Synonyms for Sway (same or very similar meaning)
WordNet sense 1 (win approval or support for):
carry, persuade
WordNet sense 2 (move or walk in a swinging or swaying manner):
swing
WordNet sense 3 (cause to move back and forth):
rock
WordNet sense 4 (move back and forth or sideways):
shake
WordNet sense 5 (pitching dangerously to one side):
careen, tilt
From the ODE community, based on WordNet
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