Consider a Kel-Tec P-32... lightweight, reasonable self-defense round, and you might be able to use fmj rounds to hunt as well as with a .22 cal. I've heard that you have to work them out sometimes, but eventually they can be accurate and reliable enough for your purposes.
www.kel-tec.com/prod02.htmI don't know about sights, but can't be any worse than the NAA weapons. I think accurate at any distance and small/light are mutually exclusive, partly due to very short sight radius and even non-existent sights on many small weapons.
I had a Walther TPH in .22 and loved it. Reasonably accurate, very reliable, but heavy at almost 12 oz. empty. Compared to the P-32 at almost 7 oz,it seems to weigh more. Neat little pistol, though, with good sights, and went bang every time. Expensive though, I should add.
www.waltherusa.net/tp.htm#Finally, I'd consider the SIG Trailside, or even a shorter barrelled Ruger in 22/45 configuration. The Ruger especially is ultra-reliable and accurate, with plenty of 'smiths able to make it do wonders while lightening it up. A fun gun I'd take out into the boonies.
Hope this helps...