I currently use a Canon A1000IS which weighs 7.85 oz all in - camera, strap, 2 AA lithium batteries, padded case, Aloksak ziplock bag. Previously I had a Canon Elph which weighed just a little less.
One important decision is rechargeable proprietary battery versus standard disposables. After using the Elph with a rechargeable, the hassle of packing or shipping a spare battery; or charging in town pushed me to the A100IS which can use standard AA disposables. I use lithiums in it - a lithium AA is .54 oz, an alkaline AA is .87 oz (requires 2). The lithiums have a much longer life.
I just picked up a StickPic which attaches to the tip of your hiking pole and weighs .41 oz - absolutely worthwhile if you solo and want interesting photos that include you! Also picked up a Joby GorillaPod Original (1.67 oz) that I haven't used much yet but looks good.