Farts are mostly particulate. So, you’d be lighter.

Edit: I did not have “researching farts” on my dance card today, but here we are - I have inadvertently repeated a misnomer. While flatulence can be accompanied by aerosolized liquid, microbial elements, and particulate fecal matter, our gut is actually much more efficient than previously thought at separating gasses. Healthy farts do not contain a significant amount of non-gaseous material. A tiny bit of such material would weigh more than the gaseous content, hence the misnomer that farts are mostly liquid and solid material by weight.

As the gasses contain hydrogen and sometimes methane, they are indeed lighter than air, on average. They may also contain sulfides and carbon dioxide that are heavier than air, but in smaller quantities.

So, according to flatus experts (yes, that’s a thing), yes, farting on Earth likely makes you heavier.

For those who want to suffer as I have, here is a fairly comprehensive article on the matter.