I’ve always thought the fact that you will soon smell a fart that originated some two feet below your nostrils (standing up, in still air) as empirical evidence that flatus is lighter than air. No need to count molecular masses, unless one wants to.
So I think the conclusion is that you gain a trivial amount of weight.
Every morning, before getting dressed, i pee and then weigh myself. The peeing is usually accompanied by the passage of some gas and I started wondering about that.