What is the effect of adding weight to a wheel vs adding it to the frame?
The answer I got was 2x -- adding one ounce (or gram) to the wheel at the outer diameter (ie, the tread) is equivalent, in terms of force/energy needed to accelerate, to adding twice that amount to the bike frame.

The answer was a bit involved and takes careful reading to fully understand, but the answer can also be explained with this thought experiment:

If you have a theoretical weightless wheel, fixed to a stationary axle (ie, not rolling on the ground), and you add a mass to its outer diameter, the energy needed to accelerate that added mass to some tangential velocity is the same as the energy that would be needed to accelerate the mass to the same linear velocity (ie, as if it were attached to a weightless bike frame).

But if our theoretical weightless wheel is not fixed on a stationary axle, but is instead attached to our theoretical weightless bike, we are accelerating the mass both tangentially AND linearly so we add the two energy requirements together, meaning it takes 2x the force to achieve the same acceleration and 2x the energy to accelerate to a given speed.

So the answer is 2x (and not 7x or 10x or whatever is often quoted).