While it is in your body, it would likely be compressed to a higher density than air

Somebody get Adam Savage, Jamie Hyneman and a very sensitive set of scales…

Well, “gas” is a pretty vague term but if you’re referring specifically to farts, they’re not necessarily heavier than air because they don’t just consist of methane and hydrogen, but other poo-particles too that are heavier than air.

The realistic answer is: The change in weight is pretty negligible, but you probably still become ever so slightly lighter.

When you fart the expelled gas isn’t immediately replaced. So you just become lighter by the mass of the flatulence. (Which will be a rounding error to the mass of your body)

Wouldn’t your volume reduce? Rather than you getting heavier…

Ignoring stuff like breathing and eating and whatever, as gas builds up from microbes metabolizing shit in your gut, your mass stays the same but you become less dense (and therefore must take up more volume, and be physically bloated by the gas). The boyant force of air trying to get under your volume and push you up is a battle between volume and mass, so since you take up more volume for the same mass, boyancy will technically reduce your weight, but probably not by much.

When you fart, the gas is released and your volume and mass decrease by the same volume and mass of the gas. Because the density of this gas is much lower that your average density, your density increases while farting, removing any extra boyancy created by holding the gas in. Depending on the density of the gas, the weight of mass you lost is more than or less than the boyancy lost

If the gas is lighter than air, the mass weight lost from farting is less than the mass weight of air for an equivalent amount of volume lost. Just like deflating a helium balloon, this results in a net loss of boyancy, making you heavier.

The opposite is true for gas heavier than air. The mass weight lost from farting is more than the mass weight of air for an equivalent volume. Just like dropping sandbags from a hot air balloon, your boyancy increases (but seriously not a lot)

As for the density of farts? They are almost certainly lighter than air because we are usually hotter than our environment (else were uncomfortable) and methane is about half as dense as typical air. Apparently it’s complicated but my impression is that farts are usually less dense.

Does this make any sense? Are we really experiencing a boyant force even when our average density is much greater than air? I dont think so, I think boyancy in air is irrelevant for humans. Here’s an interesting bit of science that helped me understand why the way we are taught about boyancy isn’t always the whole story