The airlines are a business, not a charity nor a 'right'. They transport people and cargo to make a profit. The price of a ticket is very much about need and demand, and is not calculated by taking in consideration people's weight. Cargo is a completely different matter.
On a plane you will encounter plenty of inconsiderate people, or people you just don't feel like sitting next to. What do you expect the airline to do about it? Sitting next to someone who is so large that they can't fit into one seat is a completely different issue. There's also a big difference between sitting next to someone a bit big who's rubbing shoulders with you and stretching their legs out to someone who's obese.
If a person cannot fit into just one seat they pose a safety risk to themselves and the person sitting next to them. Not to mention how uncomfortable both people will be. Many carriers in the US offer you a half price ticket for the 2nd seat if you purchase both seats at the time of booking. You also have the option of buying a business class or first class seat if that aircraft has any. These are all good options.
The airline lets passengers check in a bag as a courtesy. They don't make any profit off this, unless they are charging extra fees. It's much easier for a passenger not to pack 24 pairs of shoes for a two week trip then it is for them to lose 100lbs for their flight. Baggage and cargo has nothing to do with a passenger not fitting into one seat.
Like someone else stated, just because a large person sitting next to you is paying more for their ticket (if people paid by weight) you wouldn't be any more comfortable.
Coach class seats are very small and cramped even if you are skinny. Like someone else already stated, us consumers have driven down the cost of tickets. What do you expect? Again the airline is a business. If you don't like the small cramped seat your very affordable ticket got you then pay more and fly first class.
What difference does it make who's fat, who's skinny, and how they got that way? Why do you think the airlines care?