Summary: As our main result, we supply the missing characterization of the \(L^p(\mu)\to L^q(\lambda)\) boundedness of the commutator of a non-degenerate Calderón–Zygmund operator \(T\) and pointwise multiplication by \(b\) for exponents \(1<q<p<\infty\) and Muckenhoupt weights \(\mu\in A_p\) and \(\lambda\in A_q\). Namely, the commutator \([b,T]\colon L^p(\mu)\to L^q(\lambda)\) is bounded if and only if \(b\) satisfies the following new, cancellative condition: \[M^\#_\nu b\in L^{pq/(p-q)}(\nu),\] where \(M^\#_\nu b\) is the weighted sharp maximal function defined by \[ M^\#_\nu b:=\sup_{Q} \frac{\mathbf{1}_Q}{\nu(Q)} \int_{Q} |b-\langle b\rangle_Q |\,\mathrm{d}x\] and \(\nu\) is the Bloom weight defined by \(\nu^{1/p+1/q'}:= \mu^{1/p} \lambda^{-1/q}\). In the unweighted case \(\mu=\lambda=1\), by a result of Hytönen the boundedness of the commutator \([b,T]\) is, after factoring out constants, characterized by the boundedness of pointwise multiplication by \(b\), which amounts to the non-cancellative condition \(b\in L^{pq/(p-q)}\). We provide a counterexample showing that this characterization breaks down in the weighted case \(\mu\in A_p\) and \(\lambda\in A_q\). Therefore, the introduction of our new, cancellative condition is necessary. In parallel to commutators, we also characterize the weighted boundedness of dyadic paraproducts \(\Pi_b\) in the missing exponent range \(p\neq q\). Combined with previous results in the complementary exponent ranges, our results complete the characterisation of the weighted boundedness of both commutators and of paraproducts for all exponents \(p,q \in (1,\infty)\).