I'm thinking about weight in relation to density. If I inhale, do I become heavier or lighter? What if I inhale pure helium? Or CO2?

Its been a long time since I've studied any physics, so sorry if this is a super simple textbook answer. Anyway, here's my question(s) in many more words...

If I inflate a balloon with Helium, it floats. Obviously its average density has decreased, but its total mass has increased. The same should be true if I inhale helium. But isn't weight a type of force? So if weight can be expressed F_w=m*a_g where a_g is the acceleration due to gravity, then technically my weight should have increased, right? But the helium is also creating an upward force inside of my lungs, isn't it? Like a balloon?

In general, does density impact the way we weigh things? Is there a way to account for it? Is taking a plane from a high altitude to sea level a good way to lose weight?