Lightweight, flat batteries
Cell phone batteries are nice and flat (0.230 inches vs. 0.560 inches for AA in my phone) and have similar voltage of 3.7 volts. Mine is a bit wide though (1.440 inches). Two AA would be about 3.3 to 3.4 volts when new, so depending on the specifics the cell battery may be directly useable. They are generally Lithium Ion if not Lithium Polymer, both are as light as you may possibly find. There are general battery chargers that could work with them as well (I found one at Radio Shack, cheap on sale, $25-$30 generally as I recall.)

You could also check with a hobby store if you have one nearby, they have many types of batteries for small RC cars that may be to your liking.