Obesity rhymes with:
analyticity, animosity, atrocity, audacity, biodiversity, capacity, complexity, complicity, curiosity, density, diversity, domesticity, eccentricity, elasticity, electricity, falsity, felicity, ferocity, generosity, incapacity, intensity, laxity, monstrosity, necessity, opacity, overcapacity, paucity, perplexity, perversity, publicity, religiosity, simplicity, specificity, toxicity, university, velocity, viscosity, voracity
Obesity sounds like:
obfuscate, object, objected, oboist, obsessed, obst, officiate, officiated, offset, offshoot, opacity, opposed, opposite