Misspecification happens for various reasons in weight adjustment procedures in survey data analysis. To study the consequences of weight misspecifications, we study the effects of using a multiplicative biasing factor to describe the weight adjustments and reflect the distributional change from design/initial weights to final weights. The necessary and sufficient condition of the Horvitz-Thompson (HT) estimator of a population total being consistent is then given in a superpopulation setting. When HT is consistent, we first investigate the bias in other estimators for population totals. We show the necessary condition for bias in Generalized Regression (GREG) estimator and the resulting bias formula in the superpopulation limiting sense. We also link the bias in a model-based estimator of Zheng and Little to the failure of extrapolated model-fitting outside the sample. Both findings are validated in simulation studies. Next we find that the biasing factor affects estimators so that one particular estimator may have the smallest variance under design weights but not under misspecified weights due to variance inflation. A preliminary analysis on simulated samples drawn from a population of real American Community Survey (ACS) data illustrates the quality of fit of the biasing factor model we proposed to the ACS data with weights modified by a few calibration/raking steps.