No because the bike is making less proportional difference as your weight increases. Take it to extremes to make it clearer, ifyou weighed a ton the difference in bike weight compared to total mass would be negligible, if you weighed 1 kg the bike weight would be hugely significant.
Three stones is about 18.5kg, close to the equivalent of two bikes: how much lighter is a new bike going to be?
Sorry to be a bore, but a new bike isn't the answer.