New tires are a good decision. They will likely make the biggest difference.

Are you skinny? if you have some weight to spare, you'll lose 10 pounds really quick on a 35 pound bike. It will be cheaper then losing 5 pounds of your bike. Find some good hills.

Then, when you no longer feel like you are about to die when you ride up a big hill, you are ready for a lighter bike. Then, and only then, grasshopper, will you be able to appreciate the difference a lighter bike will make.

Is your commute hilly, or flat? If it is flat, weight won't matter much anyways.