26x1.25 or 26X1.5 tires will help. Go for the smoothest tread you can find and go for something that can take at least 80psi. You'll get most of the performance gain and keep a lot of comfort compared to 100psi. I would look online at Nashbar, PricePoint and a few others to find the best combination of price, weight, tread and pressure capability.
I'm currently using this one with good result:
http://www.pricepoint.com/detail/141...othie-Tire.htm

You don't say whether your area is very hilly. If not, don't worry too much about weight. There are not many things you can do to save a lot of weight on your bike without spending money that would be better spent on your next bike. If you are planning to do long rides in hilly terrain, you may want to start saving for that new bike soon. But in the meantime, just suck it up and work on your strength, endurance and technique. Have fun.