Only if you're naked.

This guy farts.

A balloon full of helium has more mass than a balloon without helium, but less weight

That's not true. A balloon full of helium has more mass and more weight than a balloon without helium. Weight is dependent only on the mass of the balloon+helium and the mass of the planet (Earth).

The balloon full of helium displaces way more air than the balloon without helium since it is inflated. The volume of displaced air of the inflated balloon has more weight than the combined weight of the balloon and helium within, so it floats due to buoyancy from the atmosphere. Its weight is the same regardless of the medium it's in, but the net forces experienced by it are not.

Methane is lighter than air. Methane is indeed ~16 but nitrogen has atomic number 7, molecular mass ~14, and the molecules are N2, so ~28.

The molar mass of elemental nitrogen is 14, not 7. However, its equilibrium state in our atmosphere is as N2 which has a molar mass of 28.

At room temperature methane is lighter than the atmosphere on Earth's surface, not heavier.

However, pressurized in your body it may he heavier. I see no studies measuring this.

One of those interesting facts I like and will bring up sometimes, the pound and the gram aren't just different scales for the same thing since the pound is the measure of weight or force and the gram is the measure of mass. In the vast majority of cases most people encounter in everyday life they'll be roughly interchangeable if you convert, most things being done at roughly 1g with extremely minor variations for location that won't come up unless you're doing super precise measurements, buoyancy won't come into play for majority of things most people are measuring in day to day, etc.

Sounds like solid scientific research to me, I will now carry this nugget of information as an absolute fact.

On top of the fact that the gases have lower molecular weights than air, they are also at 37°C or 310K ie ~5% lighter still.

m.. mostly?

Please discuss this with your doctor.

Unless you are in a vacuum chamber, then it makes you lighter. Also you would be dead.