The most they have charged is $100 a week, the least is $75.

That is a very reasonable amount of rent to charge, if charging rent is a given.

Beyond this charge, I also have to pay flights which can be $500 something. Also, my parents won't pick me up from/drop me off at the airport which is just on an hour away.

I would never expect them to cover my transportation. After all, where I choose to stay (be it 5 minutes or 10 hours away from them) is my choice, no theirs. Most families won't cover your transportation back home either.

Purchases since I've left have been a new tv+stereo home theatre, new 4WD dodge, and a boat (yes, a boat....they got a boat).

I smell a huge sense of entitlement here. It's their money and their finances, its' utterly irrelevant to the post at hand here. The fact that they do have money doesn't preclude you from leeching off them.

In my practical mind yes, I am a financial expense over time. I get that.

Indeed, and what they're charging you isn't unfair at all.

In my emotional mind, I don't feel welcome. When I do go home I'm usually out with friends most of the time, will buy my parents coffees etc when we're out, help out chores and help my siblings with babysitting etc. I'm not having gourmet breakfast, lunch, and dinner while running the power 24/7. Keep in mind, I do this once a year. When I add the factor that they won't do the airport thing either, well....I just feel like a tenant.

This is /r/relationships material, but you need to look at the relationship with your parents. Whether they welcome you or not goes beyond these rent-charging stuff - how do they treat you while they're there; do you get a home-cooked meal, etc?

Frankly, their charging might be just to tell you a.) be more fiscally responsible/aware of your cost on others and b.) that they want their private space, as a form of ensuring you don't spend too much time at home.