Seems the opinion is split.
Hills are where it is noticed most and to an extent it is the motor. By improving that you will perform better and if in improving that you also lose weight then so much the better. But there comes a point where the motor will not improve any more. That is when lighter parts come into it but it is not the weight loss of those parts that improves performance. It is the quality of those parts that perform better.
So get fitter and you will cycle better and hopefully there will be a weight loss to go with it When the motor stops improving- then look at the components.
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How long was I in the army? Five foot seven.
Spike Milligan