How does bicycle gearing affect mechanical advantage?

[sophiecentaur]

Surely not.
A cyclist is an inverted pendulum who positions the bike wheels so as to “fall” in the direction they want to turn. Gravitational acceleration is not dependent on the mass of the cyclist so the speed of a manoeuvre is determined by how quickly they can reposition the bike.

The fulcrum of the inverted pendulum is the line between the wheel contact patches. The energy cost of manoeuvring is proportional to the bike mass and speed² used to reposition the fulcrum = bike.

I guess you are right: that aspect of manoeuvrability is affected by bike mass (Moment of Inertia, actually) than rider mass (what about his legs, though?)
But there are other reasons for wanting a light bike. Manouvering is mainly restricted to cut and thrust competition. Just accelerating must be pretty important, surely - and going uphill. In those cases, it will be Mechanical Advantage and not Velocity Ratio that counts, though. The bike mass and friction contribute to - reduce MA.