Just for fun, I put some numbers into the bike calculator. I assumed 250W power output, rider weight 154 pounds, and a WW bike weight of 6.5kg (14.3 pounds), and a "normal" bike weight of 8.5 Kg (18.7 pounds, which is likely what mine weighs with a water bottle and saddle bag).

Anyway, the difference on a completely flat course is negligible. I think we can all agree on that.

I put in a 20Km ride with an 8% climb of 10Km and an 8% descent of 10Km. I think this is a reasonable climb one might find on a ride, either all at once or (in my area) 1 Km at a time...anyway the difference on the descent is negligible (actually the heavier bike is a tiny bit faster!), and the time saved by the weight loss on the climb(s) is a whopping 1 minute.

Now if you are racing that 1 minute difference may be significant...however for most recreational cyclists that doesn't really matter...it certainly doesn't matter to me...and I suspect (you would need a different calculator) you could save that 1 minute and more by getting a set of aero wheels.