surcharge has 9 distinct synonyms spread across 2 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.
charge an extra fee, as for a special service
fill to capacity with people
“The air raids had surcharged the emergency wards”
print a new denomination on a stamp or a banknote
fill to an excessive degree
“The air was surcharged with tension”
show an omission in (an account) for which credit ought to have been given
an additional charge (as for items previously omitted or as a penalty for failure to exercise common caution or common skill)
Synonyms, antonyms and the broader and narrower relations for surcharge come from Princeton University’s WordNet. Full sources and licences.