My FS is much heavier than my HT, however I am not sure it makes me a faster rider far from it…
If your FS was lighter, and ignoring any downsides to making it lighter, then you’d be faster.
Bike performance is made up of a number of factors, such as stiffness, geometery, comfort and weight. Just a few hundred grams can make a huge difference, so that’s why people are obsessed with it.
Of course, road bikes raced at the top level have a weight limit which is quite easy to hit nowadays, even with power meters on. But there is no such weight limit Sportives/Fondos etc.