We have grizzlies around here, and every gun expert I have talked to recommends at least a .44 magnum pistol. I haven't seen one that is light, but a 6 shooter revolver is pretty easy to handle. I carry one that has a 6 inch barrel, and loaded it weighs about 6 pounds, I would guess.
Bears have a think breastplate bone that most bullets just can't penetrate. They usually just anger the bear. While a snub-nosed .32 might knock down a black bear, or a moose, a charging grizzly is just plain hard to stop. And they charge on all fours, like a bull, not like you see in the movies. A .44 magnum round will penetrate the breastplate/collar bone and sink into the vital organs. We had a guy hit a grizzly with an arrow, and severed a major artery, and it took the bear about 15 minutes to die, but I would call that a lucky shot. A good shot with my pistol is accurate up to only about 40 yards.
Also, I would highly recommend a safety course with a magnum pistol. There are gases that escape out of the sides, and if you hold it the wrong way, you can cut your hands & wrists up. And the trigger guard can cause injuries to your knuckles if you aren't careful.
The gun may be expensive, but I would think there are plenty of folks in Alaska who make ammunition, and you don't have to pay much for it. I pay about $21 for a box of 50 bearload rounds, made about 60 miles south of me.
And you have to get used to it. Find a place where you can fire off about 12 rounds every few weeks, and get confident with it. Wear eye & ear protection, and clean it with a recommended solvent after each use. You have kiddos in the house, so you will have to consider where to keep it. Mine is loaded all the time, and never too far away. I never go into the woods without it.
I have not yet seen a grizzly bear. And every black bear I have seen has been running away from me when I see it. But I have read enough reports from around here that I know it is not far-fetched that I will bump into one some day.
Aim was great, but my instructor found it amusing. Then again, I wasn't under the fear that the target was going to eat me for lunch. 
