Low response rates due to unit nonresponse have always been a ubiquitous problem in survey-based empirical research, and calibration is a popular method to adjust for bias caused by unit nonresponse. Typically, some external information on the true population quantities of margins for some calibration variables is available, and sometimes also of higher-order interactions. Weighting algorithms try to adjust the sample to these external benchmarks. It is generally assumed that even if the underlying missingness mechanism of the unit nonresponse is non-ignorable, weighting will at least alleviate the severity of the bias. We discuss data situations where weighting under a missing at random (MAR) assumption adjusts the sample correctly but still increases the bias for the analysis model, and we describe strategies for identifying auxiliary variables that are less susceptible to these unwanted effects.