How do I know if an asphalt surface needs planing or not?
Whether to plane the surface or not before an overlay is a complete judgment call. You are comparing the general condition of the current road in combination with it's current thickness. An overlay needs to bridge underlying imperfections and absorb differential movement. The more massive the underlying tarmac, the more likely it is to overwhelm the overlay's ability bridge and absorb. Which results in the cracks and such in the old surface reappearing in the overlay.

Planing the old material off reduces it's mass so the overlay has an improved chance of bridging and absorbing imperfections. Planing alone is commonly similar in cost to an overlay, so doubling the cost of the whole job sounds about right. The risk of not doing it is that the overlay is overwhelmed and imperfections appear prematurely. The next time around, planing WILL be required. Now you've paid three times the overlay cost in a short period. Paying for planing now can prevent paying for it in the near future.

The risk of planing is spending money when it is not required. If the overlay alone can absorb and bridge imperfections adequately, it will last just as long as if it were planed first, so planing is a waste of money.

It really takes someone with a lot of experience in road work to make this kind of judgment. There's no formula where you can enter the level of damage and the thickness and get an answer. I've seen well qualified roads people argue back and forth if planing is worth it or not, so it comes down to who you feel is most trustworthy and has the experience and judgment to honestly assess your situation and make a recommendation considering your needs and not their profit margin.