The internet is awash with pseudo science which is often no more than marketing. Check out this section for the real science behind the claims. With the following books and links.
Cycling Science by Max Glaskin (to follow)
Bicycling Science by Gordon Wilson, Jim Papadopoulos (to follow)
How Important is Bike Weight?
This article demonstrates that whilst a light bike might be fun to ride and easy to handle when you are off the bike shedding grams (as opposed to several kg) isn’t going to make any huge difference to your speed uphill (where weight slows you down most).
Being significantly overweight and / or pretty unfit is the thing that’s really going to slow you down as shown in this mathematically demonstrated example by Dave McCraw.