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Synonyms for Weighty (same or very similar meaning)

WordNet sense 1 (powerfully persuasive):
cogent, telling

WordNet sense 2 (tending or intended or having the power to induce action or belief):

WordNet sense 3 (of great gravity or crucial import; requiring serious thought):
grievous, grave

WordNet sense 4 (of great significance or value):
important, of import

WordNet sense 5 (marked by great psychological weight; weighted down especially with sadness or troubles or weariness):

WordNet sense 6 (excessively fat):
corpulent, obese, rotund

WordNet sense 7 (having much flesh (especially fat)):

From the ODE community, based on WordNetadd/edit