I disagree. Let me suggest this to see if it makes sense:
First, let's assume that gravity does not change for the purposes of this discussion -- i.e., that the gravitational "constant" is indeed constant.
Now...
When you inhale, you capture molecules of air. This increases the overall mass of the "confines of your carcass" and, by definition, increases your weight (barring weird stuff like a negative gravitational constant or the inhalation of anti-matter). So you weigh more after you inhale, period.
Your buoyancy in the ambient atmosphere increases because your overall DENSITY (mass PER UNIT OF VOLUME) has decreased. The confines of your carcass are now larger; they were made larger by expanding your chest to inhale a substance less dense than your body's density before inhaling.
So, although you encompass extra molecules and therefore MUST weigh more after you inhale, your density (kg/m^3 or whichever units you prefer) has decreased. If the density of the ambient environment (a swimming pool full of water, for example) hasn't changed, you'll find it easer to float in it -- because, although heavier, you're less dense.
Hey! It just occurred to me that maybe the advice to "take a deep breath" if we're ready to do something dumb has some scientific basis -- it makes us less dense!
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