boost has 10 distinct synonyms spread across 5 of its 8 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.
give a boost to; be beneficial to
“The tax cut will boost the economy”
increase or raise
“boost the voltage in an electrical circuit”
push or shove upward, as if from below or behind
“The singer had to be boosted onto the stage by a special contraption”
the act of giving hope or support to someone
an increase in cost
“they asked for a 10% rise in rates”
the act of giving a push
“he gave her a boost over the fence”
Synonyms, antonyms and the broader and narrower relations for boost come from Princeton University’s WordNet. Full sources and licences.