Sentence weighting is a simple and powerful domain adaptation technique. We carry out domain classification for computing sentence weights with 1) language model cross entropy difference 2) a convolutional neural network 3) a Recursive Neural Tensor Network. We compare these approaches with regard to domain classification accuracy and and study the posterior probability distributions. Then we carry out NMT experiments in the scenario where we have no in-domain parallel corpora and and only very limited in-domain monolingual corpora. Here and we use the domain classifier to reweight the sentences of our out-of-domain training corpus. This leads to improvements of up to 2.1 BLEU for German to English translation.