You seem to be assuming that the volume is immediately replaced by the external atmosphere, which I doubt is valid, more likely that the volume of the person would decrease, at least temporarily. The weight of 1 Liter (assuming a massive fart) of air is 1.275g according to wolfram, so, using your density numbers above, 1.275 * 1.06/1.2 = 1.126g lighter. Measurable with a really good scale, if the 90ml fart volume is realistic (has to be more realistic I guess), that’s ~.1g,
Think of yourself as a hot air balloon with a very tiny chamber, and when you release a 90 milliliter fart, you lose a little buoyancy and sink a little. You get heavier when you fart.
You seem to be assuming that the volume is immediately replaced by the external atmosphere, which I doubt is valid, more likely that the volume of the person would decrease, at least temporarily. The weight of 1 Liter (assuming a massive fart) of air is 1.275g according to wolfram, so, using your density numbers above, 1.275 * 1.06/1.2 = 1.126g lighter. Measurable with a really good scale, if the 90ml fart volume is realistic (has to be more realistic I guess), that’s ~.1g,
No, you get denser, but not heavier.