once they are at the same speed the lighter one will use less fuel to maintain that speed, the same principle applies to bike and cyclist.
I'm with
@Stompier here. Think you're not recognising the excellent efficiency of a bicycle compared to that of a car - which is where your comparison is flawed (or at least the difference is so marginal as not to be useful). This is CycleChat for goodness sake: why are you bringing motor vehicles into it?
Since the system weight is bike + rider, a difference in bike weight will mean a rather small %age difference in system weight.
Have a play with this '
Bike Calculator'.
A rider averaging 150w over 100km on the flat (and everything else kept the same) on a 9kg bike would complete 14 seconds faster than a rider on a 10kg bike (210:57 v 211:11). On that analysis is (bike) weight "[one of the two] most important factors"? I suggest not.
If one sets the amount of climb to 1% (rather flat for Devon), then the difference is greater: the rider on a 9kg bike takes nearly a minute shorter (shock, horror - the bike is sooo much 'easier' to ride - not).
The issue with all this is riders whose fitness and strength has reduced with age yet they want to keep up and ride with 'better' riders on the hills - a light bike may give them a psychological boost (hurrah and nothing wrong with that) - but it's in the mind, not the body. Just ride steady up the hills, put a bit more effort in on the flat and let the endurance developed by many miles over many years pull the younger guys in a few hours later. Fitting 5000s would be a good way of getting an extra 15w (as opposed to Gatorskins, say).