Sooo much to go over here. But you seem at least semi-sincere, so I'll go ahead and take the time.
Here's approach #1.
Where are you getting your numbers? Below are two links that would lend one to believe that the 4 stroke turbo offering from yammi or cat are about 40 pounds heavier than you are suggesting. Or if they have lost 40 pounds in the last year or two, their marketing department has done a really good job of hiding it from everybody. Let me know where you are seeing these verified weights, I would be very interested to see your source data. In the meantime, here is two links for what I am seeing.
Second half of approach #1 is that you have chosen the heaviest of the 2 strokes to compare the 4 stroke to. The Anchorage Polaris video above mentions an RTR weight of a Polaris at just a little over 500 pounds, and I believe that might even be with a bigger gas tank than many others. Either way, you can see that from my perspective, your mention of a 69 pound difference ends up looking to me to be more like a 130-140 pound difference - roughly double the difference. I'm always interested in getting to the bottom of things and actually finding truth, so I'm not here to fight you, but I would love to see how you are seeing things so differently from where you stand. Also, one more thing here is that by the end of the day, the gas tank is empty and the oil tank is at least not totally full for a 2 stroke anyway, so the difference, even if we don't factor in the burned oil still ends up being greater, as a percentage of overall weight anyway, as the day goes on.
Approach #2:
Many would believe that your method of adding the rider weight is an "incorrect" way of looking at things. I would say that it possibly could be, depending on rider style. If your rider style is more that you drive your snowmobile like a car, then it would seem correct to add it in. But if your style is closer to riding it like a BMX bike guy doing a backflip in the air an spinning the bike on tail whips etc. then that method becomes less and less correct the more you ride like that. Caleb Kesterke is the closest thing we are currently seeing to a guy who rides his snowmobile more like a BMX bike than like a car. But lots of us are trying to head more in that direction. We just aren't freaking freaks of nature like Caleb is - man that guy is incredible.
In the mountain bike world, the really light cross country bikes are maybe like 25 pounds while the really heavy downhill bikes are more of a ballpark of 35 pounds. If we were to add in rider weight, that difference would be a really small percentage. But it doesn't make sense here to add in rider weight, and so really the percentage is like 30-40 percent, and you end up getting people saying how light their cross country bike is and how heavy their downhill bike is, even though it is only 10 pounds.
Approach #3:
I will try to find a nicer way of explaining what
@bnorth was probably trying to say and that is just real life experience of trying it out. I consider myself really average at 5'11" and 190 pounds. I am having so much fun on Polaris for the last 4 winters, and I credit a bunch of it to the weight and then some of it also to Polaris just having the geometry really figured out with this Axys platform. A lot of days that aren't quite as deep, if the 600 was 25 pounds less than the 800, I would actually even pick it over the 800 because I'm just discovering that every single pound taken off really does just make a really big difference, at least to me. Once again, though, it totally depends on riding style as well. I'm in trees and technical stuff most of the time these days. If I was in more wide open areas, I might very well feel differently. I've seen videos of BC, and I'm almost sure I would choose to buy a different sled if I lived up there. I live in Utah, where more often than not, it isn't ridiculously deep, and you have to go pick your way through trees just to find anything that is fresh. Anything close to these conditions, and suddenly power to weight ratio doesn't mean a thing. All that matters is weight. Any sled out there has the power needed, pretty much, and it's just a matter of weight to determine how long I can last before being completely pooped as I am after all average, which means I work at a desk all week to be able to afford this nonsense.
It becomes one of those things where, until you have really gotten into the trees and spent all day there, I can easily see how it would be hard for you to understand why some guys are placing such a high premium on the weight. You have to spend a season doing it before it makes sense why we act the way we do. Honestly, I hear the same thing about my mountain bike. I spend an extra grand or two just to get another 2 or 3 pounds off of what would have been pretty much the same bike and folks really don't understand it. But after years of doing it, I wouldn't have it any other way.
Hopefully this helps.