I do not have the engineering data to corroborate, but on my car with a full tank of fuel (16+ gallons) there is considerable balancing of my vehicle noticed at the rear end.
Mathematically that comes out to approximately 112lbs of fuel. Some readings on my car say it is a 55/45 F/R weigh ratio.What I am not clear on is if the manafacturer is basing that on a loaded/fueled car, or empty curb weight? Then again, 112lbs is barely one adult passenger. Without real test data, my feelings could wholly be placebo?
Furthermore my car is prone to fishtailing depending on the (in order of effect) driving style, road conditions, and tire type.
Anyway from my by gone experience in the automotive rubber industry the best effect will be winter tires hands-down. My useless Camaro in snow was able to take down blizzards and snow drifts driving uphill past *stuck* over-confident 4WDs. You still have to drive extremely carefully, but the snow tires will get you home with high traction.
I used the Blizzak WS50, non high-performance design (unlike The Dunlop WinterSpors, etc), but very well regarded in Scandanavia actually. Cheapo Winterforce Sears tires are also great, sans the Sears installers.