Personally, I can cast higher line wt’s farther with the same rod.
I’ve cast a TiCr in 5, 6, 7, and 8 wt sizes, all 9 ft rods and basically the same action. I didn’t put a tape to it, but I can get more distance with the 8 wt than I can with the 5 wt. (Fishing shows are great for getting to “test” several rods.)
My 4 wt and my 7 wt rods are different brands, but both are 9 ft rods and the actions are almost identical. I top out with the 4 wt at about 60 ft of line, while the 7 wt tops out just short of 80 ft. These casts are on grass, while practicing.
I have no idea how you would quantify the difference in distance between line wt’s, but with everything else being equal, I can get more distance with the heavier line wt’s.
Just my 2 cents worth,
Rex