I know this may not be not exactly lightweight, but i use disposable cameras for my outdoor photography.
I made the switch when i first started out going camping, I went out on a 24 day trip with my friend. With a stroke of bad luck, he ended up accidentally dropping his little point and shoot and wrecked his $150 camera (albeit he could have been a little more careful to his camera). From that experience, i just started to use little disposable cameras whenever i venture out.
One benefit that I have noticed that disposable cameras have over point and shoot cameras would be that i never have to worry about the battery life of my disposable camera. I have noticed that on some of my longer duration trips, most of my friends usually run out of battery life on their camera before their trip is over, sometimes missing some breathtaking scenes. Plus in some respects, I have noticed that disposable cameras are sometimes lighter than some traditional point and shoot cameras. Although, i dont have all the fancy little options that a basic point and shoot camera would have, IMO i believe that they are a little more rugged in my experience.
I recommend the cheap Fujifilm disposable cameras (I think their lighter than the kodak ones). I've also had good experiences with their disposables and underwater disposables.
But please note that if you can get over the "bulkyness" and the "fashion statement" of the underwater disposable cameras their fairly well built and bombproof.