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Synonyms for Weight (same or very similar meaning)

WordNet sense 1 (a system of units used to express the weight of something):
system of weights

WordNet sense 2 (a unit used to measure weight):
weight unit

WordNet sense 3 ((statistics) a coefficient assigned to elements of a frequency distribution in order to represent their relative importance):

WordNet sense 4 (the relative importance granted to something):

WordNet sense 5 (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):
exercising weight, free weight

WordNet sense 6 (weight down with a load):
burden, burthen, weight down

WordNet sense 7 (present with a bias):
angle, slant

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