I recall doing an experiment in high school where we weighed a balloon that was blown up vs deflated. The one that was blown up weighed more, but by barely anything.

Assuming gas composition and compression and moisture and temperature of breath are the same as a fart, then yes you lose weight.

But methane is lighter than air, and there are so many other variables that it’s possible a fart would make you lighter. However that’s because of boyancy, you are losing mass plain and simple.