I know most of the responses here have been about stand alone cameras, but has anyone given thought to a camera phone? I know the quality isn't the same, but if you're really looking to lose some weight, it's a valid option.
I'd suggest a Nokia N-series phone, like the N82 or N95. You get a phone (of course), 5mp camera and video recorder, GPS with maps built in, radio, alarm clock, and 8gb of storage space. If you think you need it, you also get a high-speed internet device and music/media player.
If you opt for the newish N78 (3mp camera), or any of the forthcoming N79, N85, or N96 (all 5mp cameras), your pics are tagged with gps coordinates, too. Makes it easy to figure out where you were when you snapped the shot!
If you keep the phone off, and only turn it on when you need it (take pictures, use gps, etc), the battery will easily last well over a week.
They range from 3.4 to 4.5 ounces.
Price is the only concern. You generally can't get Nokia phones subsidized by U.S. carriers (AT&T and T-Mobile), so you pay full price. N82 ~400, N95 ~520, N96 ~850 (suggested price when it arrives in October).