Bike weight affects the "feel" and handling of a bike to a degree, but usually the differences in bike weight discussed (like maybe 2-3kg between super-light and fairly heavy road bikes) are not that significant in this respect. Riding on nominally flat terrain I wouldn't expect to pick up any time on a lighter bike. Only climbing is a real advantage and time gains are easily predictable by simple Newtonian physics over any course. For example I'm doing a 100 mile ride this weekend with around 4k elevation change. Predicted finishing time at my average endurance power is 7 hrs 35 mins. If I drop my bike weight by 2 kg the model predicts a saving of 4 mins. That's with 4k of vertical climbing! Running the same calculation on a much flatter 100 mile course, I would gain just over 30 seconds with the 2kg lighter bike. Basically nothing worth spending any money on.