The "what ifs" and hypothetical situations involving theft are probably endless. It's reasonable to assume that your bike will be safe in a town with a population of 39. It's also reasonable to assume that another person will leave your bike alone, since it doesn't belong to him. Obviously, people with light fingers don't employ that form of reason. Sadly, light-fingered people can live anywhere, even small-town America.
The original question seemed to center on whether or not to carry a lock when traveling ultralight and solo. If you're alone, there won't be anyone else to watch the bike for you when you're in a store. There might be unplanned contingencies when you're forced to leave the bike, for whatever reason. Personally, I don't worry what others might think if they see me lock my bike. I feel that I can afford to be friendlier and more open knowing that my bike is secure. I'm more apt to linger in a cafe or stay and chat with someone I meet if I'm not thinking about the bike. Going solo, I'd always have at least some means to secure my bike. When and where you choose to use it could then be up to you. Chances are that you'll be traveling through towns where theft does occur, at least occasionally. With some of the light-weight cable suggestions offered by others, I doubt you'd even notice the weight on your bike. And I second DaveB's suggestion of a combo lock. Not only is there no key to lose, you'll save weight by not carrying one! The other deterrent to theft is just using your smarts and being aware of your surroundings.