I have the small Gerber hatchet mentioned. IME (in my experience), a small axe or a hatchet is not worth's it weight, nor is it big (pun intended) either in the performance category. You have to exert a tremendous amount of energy to chop anything of a slightly larger size with the small axe/hatchet. The retracting 4oz saw (6" saw blade i think it is) Gerber makes is so much more useful. There are other longer saw options that still weigh less then the smallest hatchet. The saw cuts wood so much faster than the small axe or hatchet. The small axe or hatchet makes some nice little chips which are useful as kindling. A sturdy knife blade can easily make fuzzy sticks to perform the same purpose.
It's going to take 2+ lbs to get into the true small axe category. Even then, a longer, heavier axe is what you really want for a good camp/cabin axe. If you want a fine camp/cabin axe, Gerber makes those. For general backpacking though, go with the Gerber Saw. oh...if you primarily use rivers as transport, then maybe a longer, larger camp/cabin axe (3-4 lbs) would be 'ok' - especially if your portages are not too long.