Weight won't make a difference, at least as far as bang-for-the-buck is concerned if you're sticking with that frame. If you REALLY want a lighter bike, get a modern road frame. Trying to make that bike light to improve speed on the road would be like trying to strip weight out of a Jeep to improve it's drag strip time. It's just not a drag car!
(Regardless, the biking community (at least some parts of it) are way too concerned about weight, IMHO. I'd challenge anyone spending big bucks to reduce weight with this: Put two water bottle cages on your bike. Have a friend set up 4 identical-looking bottles: Two that are full of water, and two that are empty. Then, go for several rides - in between, have your friend switch randomly from full bottles to empty bottles on your bike without telling you which is on which run. With 24 oz bottles, that's several pounds of weight difference - however, I bet most people wouldn't be able to tell the difference of riding with the full bottles vs. the empty ones.)
If, however, you're only interested in going a bit faster on the mostly smooth surfaces you frequent, do what these guys suggest and get some narrower, smoother, higher-pressure tires.