Why are fast blow fuses more tolerant to small over currents than slow blow fuses?
That is a nice observation - I am only speculating here about the how, and I hope a fuse manufacturer will jump in with a better answer.

The fast fuses I looked at contain a relatively thin wire, slack, while the slow blow fuses contain a thicker wire, held under tension by a spring.

As such, they operate in different ways : you need to melt the wire in the fast fuse, to break the circuit. But the slow blow fuse only needs to soften the wire until it yields under the spring tension, at a somewhat lower temperature (for the same wire material). That leads to the use of a thicker wire, as can be confirmed by observation.

Thus the fast fuse, with its thinner wire, has better cooling - greater radiating surface per unit mass of material - than the slow fuse, as well as requiring a higher ultimate temperature before failing. 

So a modest overload will leave it at a high enough temperature to radiate away enough heat energy to limit its temperature, or at least slow its temperature rise, and delay its melting.