Retrospectively collected duration data are often reported incorrectly. An important type of such an error is heaping — respondents tend to round-off or round-up the data according to some rule of thumb. For two special cases of the Weibull model we study the behaviour of the 'naive estimators', which simply ignore the measurement error due to heaping, and derive closed expressions for the asymptotic bias. These results give a formal justification of empirical evidence and simulation-based findings reported in the literature. Additionally, situations where a remarkable bias has to be expected can be identified, and an exact bias correction can be performed.