Put one of your arms in a sling, and wince in pain whenever your seatmate intrudes on your personal space, or hold a hook in one hand so it looks like an artificial limb, as people get really hypersensitive about being caught noticing disabilities.

I suppose my question is: how FAT are we talking, here? Like 200-250 pounds? Or, "knock down a wall, rent a forklift" fat? I wouldn't want to deny either person a chance to travel, but I also wouldn't want to be stuck next to the really big person, or have to climb over them in the event we had to use an emergency exit. If they are THAT big, the only place wide enough to give them girth room is likely to be next to an exit.
Even when I was underweight and even before airlines started incrementally making seats tinier, airline seats were not comfortable. My complaint was mostly due to long limbs. When your arms and legs are long, it makes you ache to sit folded up like a beach umbrella or a preying mantis for 8 hours.
Honestly, I have avoided air travel since 9/11, because I don't like my stuff pawed through and my shampoo and nail clippers being regarded as terrorist weapons. Also, airlines are inconsistent about whether ferrets are allowed.

Even before 9/11, I saw road trips as a chance to be blissfully alone with my music, operating on my own time and schedule, taking my own routes, and so on. I'd driven from Atlanta to Chicago (two days, stop off in Indiana), from ATL to New Orleans, from NC to Nevada (three days) and back (four days), from Savannah to the Blue Ridge Mountains, from ATL to Tampa, and ATL to Cincinnati, for instance. My car at the time was a Geo Metro convertible that got an umptillion miles per gallon. Alas, it died after an asshat rear-ended me. 6-8 hours on the road isn't too bad. I prefer not to exceed 4-5, though.
I also prefer to drive really late at night, when I am often one of only a handful of other cars on the road. Since I've had idiots total two of my cars by running into me, and more idiots sideswipe my current car while it was PARKED, there may be some accident avoidance going on there, too.