A lighter bike is going to help most on the climbs as that's one of the areas where you notice weight so it might make a small difference depending how much weight you can shed. As posted - staring from a dead stop is easier on a lighter bike and the bike will feel nimbler because it's lighter.
If you are at your peak performance then naturally you have to start looking for marginal gains in other areas so it would then be wise to look into marginal gains in areas such as the wheels.
There are also other factors at play such as your overall health. Whether you've had enough sleep or are hydrated enough on or day or another. These things will affect your performance.