weight has 11 distinct synonyms spread across 7 of its 10 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.
the vertical force exerted by a mass as a result of gravity
sports equipment used in calisthenic exercises and weightlifting; it is not attached to anything and is raised and lowered by use of the hands and arms
the relative importance granted to something
“his opinion carries great weight”
an oppressive feeling of heavy force
“bowed down by the weight of responsibility”
a system of units used to express the weight of something
(statistics) a coefficient assigned to elements of a frequency distribution in order to represent their relative importance
weight down with a load
Synonyms, antonyms and the broader and narrower relations for weight come from Princeton University’s WordNet. Full sources and licences.