Interesting discussion here. Here are some things to consider:
** Disclaimer: I am by no means an expert, just trying to convey what I've learned myself! **
By the way, the technical term for the tires sliding is called: SLIP ANGLE. There are three different slip angles your car exhibits: front wheel slip angle, rear wheel slip angle, and whole car slip angle (read: 4 wheel drift). Read more about it in Henry Watt's book mentioned below. (General definition of SLIP ANLGE: the difference between the direction X is pointed in, vs. the direction X is actually moving, ie sliding)
1. You lost 65 lbs. So your 2800lb car (approx) now weighs 2735lbs, or 97% of it's original weight. That loss in weight is really negligable. Also: loosing weight in a well balanced (50/50) car can be tricky: if loosing the weight causes a 60/40 weight distribution, your handling will suffer. Your feeling of improved acceleration is probably a "seat of the pants" dyno: do some timed runs with and without the weight, and you'll probably notice very little, if any, change. So: weight savings can have an adverse effect on your car's handling! (Note: that's why many people stress corner balancing over loosing weight!)
2. Weight (or lack thereof) is not the only factor in handling. You already mentioned sticky tires. There's more: suspension, tire setup (pressure, camber, caster, toe-in...etc), balance, power, and don't forget about the driver! When you start to factor in all these variables, you'll see that your quest for loosing weight won't make much of a difference at all. Again.
3. With all these different factors coming into play regarding cornering and performance driving, it is important to move forward slowly: changing one thing at a time, and carefully evaluating how the change helped or hurt the capabilities of your car. It is also best to start with the cheapest stuff first too. BTW: I have a feeling that loosing more than 65 lbs in your car is going to start costing: not just money, but the 50/50 balance of your car.
4. So, what's the best thing to start with?
THE DRIVER! Learn to drive your car to it's ability, and once you've done that (which could take many years), you can slowly start to modify your car's geometery. If you're not a consistent driver, you won't understand how changes alter your car, and if the changes improve or hurt your car's dynamics. Understand your car's stock setup (it's really not a bad setup, afterall), and once you can drive your car consistently to it's limits, then it's time to play.
5. The best way to improve your
driving abilities is to attend autocross events, and DE track events. I suggest autocrossing first, so you can get the feel of your car before you kick up the speed a notch or two

! Track is more expensive than autox, so the more you learn before you drive on the track, the more effective your money spent there will be. I have seen too many beginners get all the goodies (sticky tires, suspension changes...etc) and get blown away by a great driver in a bone-stock setup car!
6. If you are interested in your car's handling, read some books about it. A couple I suggest:
Secrets of Solo Racing by Henry Watts.
Bob Bondurant's Performance Driving Handbook by Bob Bondurant.
Tune to Win by Carroll Smith: gets into the geometery of suspension, tires...etc.
While the physics you talk about make sense in the classroom, things are a little different when the rubber meets the road.

-Zoltan.
Gallery updated 01-20-02: