Tone arm resonance and cartridge compliance: How do they interact??

lewm, I agree and disagree with different parts of your statement. Rather than cut and paste a text on mechanical amplifiers and resonance, please tell me how adding weight at the headshell is beneficial to the resonance of the lever?

I agree that increasing the mass of the lever (arm tube) will dampen a mechanical amplifier. But increasing the resistant load will have the opposite effect, decreasing stability and increasing secondary effects (hysteresis, etc.) Ideally, you would change the mass of the tonearm buy using arm tubes of differing weight and matched headshells. Some manufacturers used to do this.

If you are going to stabilizing mass to most conventional tonearms, adding it as close as possible to the pivot point will both increase stability and lower resonance.

I’ve used my Stanton 881s on my Ikeda 407 with a light headshell. And with the counterweight all the way in I can’t balance it with the dynamic balance off. When I add dynamic weight I can only add a half gram to be correct.   Even though this is wrong I agree with  @lewm  and really like how this cartridge sounds on the Ikeda than on my lighter  tonearm. My speakers do reach very low bass response and I do get some woofer pumping with this setup. My woofers face backwards so I didn’t notice at first. I don’t think this is very good for the speakers and no longer use this setup. Do you @lewm get this woofer action at all using your FR arm in this way. 

The different size counterweights are supplied so you can counterbalance different weight (mass) cartridges. You can not control resonance with different mass counterweights because once the cartridge is balanced you wind up with the same effective mass regardless of counter weight mass.
Now Raul, unless you are blind measuring resonance points with a test record is painfully easy. Your comment would leave me to believe that you have never set up a cartridge correctly.

The problem with calculations is that there is enough variation in tonearms and cartridges that the published specs may be off a little.
The record tells you what is really happening. But the resonance is not a sharp peak. It is a bell curve. The point where the cartridge starts bouncing is what you pay attention to. You know you are close when you hear the warble. Using the test record also gives you an idea of how severe the resonance point is. Some combinations barely move at the resonance point while with others the cartridge almost goes air born in which case it might have to be changed. I suspect it is a matter of damping.
Moment of inertia is different then effective mass. Longer heavier arms have higher moments of inertia. This really only creates issues following warps. If records are stored correctly very few should be significantly warped. Vacuum hold down and reflex clamping solve the problem under any circumstance. 

there is another moment - most of tonearms do have rubber gourmet or other means to isolate counterweight (s), so it has it's own resonance which can be measured.