hover has 8 distinct synonyms spread across 4 of its 5 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
be undecided about something; waver between conflicting positions or courses of action
“He oscillates between accepting the new position and retirement”
be suspended in the air, as if in defiance of gravity
“The guru claimed that he could levitate”
hang over, as of something threatening, dark, or menacing
“The terrible vision brooded over her all day long”
Synonyms, antonyms and the broader and narrower relations for hover come from Princeton University’s WordNet. Full sources and licences.