Is it possible that the availability of good plumbing has contributed to our national weight gain? This may sound ludicrous, but think about it for just a moment. Very few people have to trek through the night to use an outhouse anymore; furthermore, restroom facilities are readily available just about everywhere — which means you don’t have to worry about getting rid of your waste, which frees you up to consume as much as you’d like.
As a kid, I remember taking a long bus ride to New York City for a ballgame. There was no bathroom on the bus. No one on the bus was drinking anything either. (Yes, this was before you could readily buy bottled water; but there were such things as cans of soda.)
A few times in the recent past, I’ve rented a summer house with no garbage pickup. This meant not only paying for how much waste you produce, but also storing your trash until the one day that the dump is open. During these times, our behavior changed radically: not only did we compost all our food waste to cut down on stink, but we thought about everything we bought before we bought it to make sure we wanted to deal with the waste. As a result, we bought a lot less.
I know of no legitimate research connecting plumbing and obesity, though I would be interested in hearing from anyone who does.
I'm not really sure where to begin on this one. Even if this were a factor, I think the low cost of high density calories through agricultural subsidies would dwarf any effect. Furthermore, this argument could be made about any technological advancement made in the past century. For example, cars have caused people to walk less, therefore consuming less energy daily, thus, cars cause obesity. Clearly, the argument is too simplistic. While an interesting thought, I can't imagine any serious scholarly work has been done on this topic.