I do care about the weight of my knives, and it becomes an intrinsic consideration along with form, function, activity involved, etc, etc. That is why the whole "one knife only" concept makes absolutely no sense to my way of thinking. There is a place for big heavy knives, and a place for small lightweight thin knives, machetes and the rest. The heavy egress knife that I carry in my airplane is not the knife I choose for running the mountain trails.
There are many preconceived ideas out there that associate ultra-light backpackers with a contrary mentality about a number of equipment choices as if it involved their ethics and political persuasions. Ultra-light backpackers just simply prefer to make ultra-light choices. Simple enough, in most cases. As an ultra-light backpacker, I choose to carry a lightweight fixed-blade on the trail. Some of my partners carry only lightweight folders. Some are politically liberal, some are politically conservative, or in-between. To stereotype ultra-light backpackers as "knife haters" has no validity whatsoever in my experience. I have backpacked thousands of miles with ultra-light backpackers and honestly never met a knife hater on the trail. Generally, "knife haters" are people who have had little positive exposure to knives. Seems they might have some preconceived ideas, too.

Successful 'long-distance' backpacking is about managing ounces, not pounds. If you are just going out a few miles with a pack, it doesn't really matter. I even haul a good-sized lawn chair 5-miles back into one of my favorite fishing lakes. On the long trails, excessive pounds can get you hurt - not to mention the lost needed calories burned and the sore muscles.
In the mountains where we live (we live right smack on the edge of the largest wilderness area in the state. Last house on the road to have electricity), there is a considerable elevation difference between our back 300 acres, and the front acreage. If I walk down the mountain to the lower property, I'm truly thinkin' "lightweight" knife. Though I run my tredmill almost everyday, hauling a big heavy knife back up that hill isn't my idea of fun. Nor, is it necessary. Carrying a heavier knife in one of the saddle bags is fine if I choose to ride. "Best all-around" in this country would be a 4" blade...sort of like 7 X 35 or 8 X 30 binoculars.