taking or using something in a greedy way without sharing it with others; also a nautical term for the sagging of a ship's hull.
From 'hog,' Old English 'hoga' (a pig). The meaning 'to take greedily' comes from the pig's eating behavior (around 1800s). The nautical term is related but may have separate origins from 'hog' as a verb meaning 'to arch.'
The nautical 'hogging' is actually the opposite of 'sagging'—if the ship's ends droop down while the middle stays up, that's hogging; if the middle sags, that's sagging—and old wooden ships had to be built with both problems in mind.
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