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if it doesn't have to be a bolt gun , a rossi 1892 levera ction chambered in 454 casull would fit the bill ..... they are also well under 6 pounds , and hold around 9 to 10 rounds .
If its for big bear defense I'd stay away from any hi velocity magnum. Go for a .458 caliber. Slower more frontal diameter and will have that drastic penetration needed at short range. Sorry I don't know of any under 6lbs.
Similarly, you may wish to consider a Remington 673 in .350 mag. This is the updated 600/660 based on a model 7 action. I have one and it's possibly my all time favourite rifle. They come in around the 7 lb. mark and sport a 22" barrel. It is referred to as a 'Guide Gun'. There was one here on the EE last week...
Model: 116 Alaskan Brush Hunter, a little over on the weight (advertised 7.6lbs) but 18" barrel chambered for 338 win mag or 375 ruger in stainless/synthetic.
If I had to carry a 6 pound rifle chambered for any of the established big bore dangerous game cartridges I'd sooner just let the bear get me, I mean really, how bad could it be . . .