supporting has 3 distinct synonyms spread across 3 of its 3 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.
furnishing support and encouragement
“the anxious child needs supporting and accepting treatment from the teacher”
the act of bearing the weight of or strengthening
“he leaned against the wall for support”
Synonyms, antonyms and the broader and narrower relations for supporting come from Princeton University’s WordNet. Full sources and licences.