Pretty simple answer, you're still using Wrath gear in the majority of your slots. By 82 you should have replaced almost everything via quests, especially that weapon.
Your armory says you've done all of about 6 quests in Cataclysm on the way to 82, though. That really needs to change, you can't expect to keep hopping into Cataclysm instances with lower health than an average bear tank had at level 80 and not have people get upset about it.
You are 82. My advice: hold dungeons for a while, do tons of quests, as soon as you ding 84 go to Twilight Highlands and do ALL the quests there. That should give you all you need to start running normal dungeons.
I am almost 83 and I'm in all Cataclysm gear. Mostly greens but several blues from instance runs and I only have about 61k in Bear form as well. It has made for some interesting encounters. Would the problem be that we just won't get gear that gives us that kind of health until later? Please have a look and tell me what you think.
Your base health (i.e. naked, talentless, and minus your bae stamina) skyrockets from 80-85. I believe most classes have base healths around 39k-44k at 85. So your health will rise both as you get Cataclysm gear and as you gain levels.
From the beta, my premade mage had about 80k HP. This is with some purples and high level blues, but the point is that Cataclysm gear and leveling 81-85 increases your health drastically, just leveling a 2-3 levels with WotLK gear won't change your stats much.
Don't worry about the HP at the moment. Keep doing quests, do a dungeon or two when you want, you should be fine. Once you hit 85, then you should worry about your health(not that we should even be gemming straight stam at 85 though).
Make sure you do quests in Uldum/TH once you hit 84, you'll get gear there and you'll be fine.
I had about 165k last night in our 10man, I have a 337 ilvl average and one stam trinket, one agi trinket.