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In this paper we prove weighted norm inequalities with weights in the 
${{A}_{p}}$ classes, for pseudodifferential operators with symbols in the class 
$S_{\rho ,\delta }^{n(\rho -1)}$ that fall outside the scope of Calderón–Zygmund theory. This is accomplished by controlling the sharp function of the pseudodifferential operator by Hardy–Littlewood type maximal functions. Our weighted norm inequalities also yield 
${{L}^{p}}$ boundedness of commutators of functions of bounded mean oscillation with a wide class of operators in 
$\text{OPS}_{\rho ,\delta }^{m}$.
