My road bike's stock wheels were 2000 grams for the pair. (Not including the cassette cogs, tires, tubes, or quick release, of course). After 15,000 miles (25,000 km), some of the rim spoke holes developed stress cracks, and one spoke nipple pulled partway through the rim. So I got a nice pair of replacement wheels.

The new wheels were 1550 grams, 450 grams or 1 pound lighter. The difference was subtle, with the most noticeable change showing as faster steering response on sharp handlebar movements. I suppose the acceleration was a little quicker, but not obvious. The new wheels "seemed" faster, but of course, I never did a double blind test.

So: the wheels were nice, but not a huge change.

Tires!
What tires do you have now, and what size?
What do you weigh, and how much air pressure are you using?

The more expensive road tires have thin, flexible sidewalls, and grippy rubber compounds. When the tires are at the appropriate pressure for the rider's weight, they flex over rough road surfaces instead of vibrating or bouncing the bike and rider. And the handling on turns is much better, both from grippy rubber and less bouncing on rough spots. Really, the difference is huge--this is by far the most effective upgrade.

So far, on the thread comments:
3 votes for good tires.
1 vote for no-name carbon rim wheels. On a hybrid. (Those wheels don't look bad for a racing bike. But they are 1/3 or 1/4 the price of name brand carbon wheels, so there's some risk of possible quality problems. )