People do loaded down bike tours over mountain ranges.
A light bike matters if you pick it up and carry it. I live two flights of stairs above the road, that's when weight matters to me. My current bike is a couple pounds heavier than an older one by the same manufacturer and I'm faster on it. For several reasons that would probably bore you. A light bike can be a little easier to handle in some situations that might amount to half a percent of the time you spend riding, but can be fun.
Weight in and of itself isn't a great reason to choose one bike over another for recreational/fitness cyclists. If you get paid based on race results in the Alps it's a different story, not for the rest of us comfort is way more important, and even liking the way it looks may be more important. I mean, any price range you're looking at will have broadly similar bikes, it's not like you might buy one at 17 pounds or a different one that's 35 lbs.