I like my camera to be able to fit in the hip-belt pouch on my backpack, so that it's easily accessible. I'm not overly concerned with weight if it fits.
However… what is critical to me is that I be able to use the camera for the whole trip. Meaning it has to survive rain, mud, rivers, falling. It is so nice to be able to go not just hiking – but also for example kayaking – and use the camera for the whole trip because it's waterproof and it just doesn't matter if you drop it in the river. Or to be able to take those pictures of cooking on a zip stove in a pouring rain storm. Even just the peace of mind of not worrying that I might be out several hundred dollars if someone accidentally drops the camera in mud while handing it from one person to another.
I went through a bunch of waterproof cameras and my current one is the Panasonic DMC-TS3 (current model DMC-TS4, $300). It weighs 6.9 oz if you're curious. It takes awesome photos and has built in GPS. I dropped it in the snow just today while snowshoeing.
I can't imagine switching back to a non-waterproof camera and missing out on all the extra photos.
On the "ultra light" topic… if you really want ultra light and can find a camera called the "Pentax Optio WPi" – get one. It's a waterproof camera from Pentax that they made in 2006. It took the best pictures of any waterproof I tried until this new Panasonic, and that includes compared to even some recent model Pentax waterproof cameras. I have thousands of awesome photos from it – and it weighs next to nothing. My Dad is using it now in Jakarta so I can't weigh it, but I found a review that says it weighs 3.6 oz.
