Why does reducing bike weight have such an impact on speeds? I am trying to understand the physics of bike weight.  I have just made a switch from an 11Kg road bike to an 8Kg one (obviously there are many more factors and differences between the 2 bikes other than weight), and have noticed the benefit of reduced weight.  However I am not sure I understand it.

Let's say for example My combined weight is 8+75 for a total weight of 83Kg.  The difference between this and 86Kg is minimal, but is does make a difference seemingly beyond what I would expect.

Assuming I could equalise the total weight by carrying a pack or particularly heavy bidon/saddle pack) such that the combined weight could be the same, why is the lighter bike always seemingly faster?

I have read something about rotational mass, which seems to indicate that it's nothing to do so much with your combined weight as perceived through gravity, but with the equivalent lifting effort of the moving parts, namely your wheels, and in fact it's wheel weight that is the major factor because your are in effect having to lift half the wheel in order to produce forward momentum.  Is this a sort of gyroscopic affect whereby the easier it is to turn your wheel the faster you go?
The two major "drags" on a bike, on level ground, are the rolling resistance of the tires and the wind resistance of the bike and rider.

In general, up to a point, a tire with higher pressure will have lower rolling resistance, as will a tire with a smoother tread.  Tire width also figures in, but mostly in terms of how it influences pressure and tread.

Wind resistance is affected by tire width, number of spokes, tube size, and rider position.  Generally, as the "raciness" of a bike increases, tire width and spoke count decrease and rider position becomes more prone (and hence more aerodynamic).  Tube size doesn't tend to vary much (and may actually increase as you go steel->aluminum->carbon) but that effect is slight and subtle differences in frame design can be more significant.

There may also be ergonomic changes -- eg, the more prone riding position, while more fatiguing, is often somewhat better for peak power output.

Bearing quality hardly figures in at all.  Even cheapo bearings have very low losses, and the difference in drag between them and top-of-the-line bearings is not likely to be measurable.  (The bigger difference is in durability.)

Bike weight only comes into the equation when one must "climb" (and to a very minor degree for rolling resistance), but of course it's rare to have a route that does not go up/down by 0.5% or so most of the time.  That 0.5% increases the power required to hold a steady speed by about 10% over a dead-level course.  But the 3KG difference between the above two bikes would amount to about a 0.4% power difference on that 0.5% slope.