You want to get a pair of tubular wheels. Any clincher rim is heavier because the arms that come up from the box section of the rim to hold the tire bead adds weight. And makes the tire less compliant - which translates into being less comfortable and more likely to get pinch flats. Before the later part of the 70's all good bikes used tubulars. 27" wheels/tires were big and heavy and clunky by comparison.
The lightest 700c clincher rims weighed over 400 grams each. Mavic came out with the 1st ones around 1976? There are many classic era tubular rims that weigh less than 300 grams each. If you bike is older than 1975, it would have come with tubular wheels.
The good news is that nice tubular wheels are inexpensive because the demand is for clinchers. Tubulars are like stick shift cars, they work great but people without any experience using them don't want them.