For the solubility of AB2, Ksp=[A][B]^2=x*(2x)^2. Why is (2x)^2 not considered double dipping?
It's easy, if you consider:

$$\ce{AB2 &lt;=&gt; A + 2B}$$

It's solubility equations would be:

$$K_{\text{sp}}=\ce{[A][B]^2}$$

That equation follows from the law of mass action. 

If you consider the amount of A as $x$, wouldn't the amount of B be $2x$ obviously? 

If your issue is with why it's squared, it's just the equilibrium law, it follows from law of mass action. You can't really argue why the square is there.