To make worse or more severe; to intensify something negative. In formal usage, it means to worsen a situation rather than to annoy (though the latter is common in informal speech).
From Latin 'aggravare,' combining 'ad-' (to) and 'gravis' (heavy), literally meaning 'to make heavier.' The original sense was physical weight, but by the 16th century it had extended to mean making problems or conditions more burdensome.
Remember the Latin root 'gravis' (heavy)—to aggravate is to add weight to a problem, making it heavier and harder to bear. Don't confuse formal 'aggravate' (worsen) with informal 'aggravate' (annoy)!
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