Answer: If the weights for the two cohorts are fairly different, the combined model will be heavily influenced by the cohort with the larger weight, and the results may not be as expected since the combined fit will closely mimic the level and number and location of joinpoints for that individual cohort. In this case the statistical algorithm is appropriately weighting the series that is more reliable. In some cases, however, it may be more appropriate to weight each series equally, even though one series has a larger variance. For example, it may be appropriate to weight two racial/ethnic groups equally if the goal is to find the best fit for two groups ignoring the fact that one series is more reliable than the other. In such a case, running the unweighted model using the Heteroscedastic Errors Option of "Constant Variance" may be more appropriate. These same considerations are less obvious but can be relevant when fitting a parallel model. In this case, level is not an issue (since each cohort has its own level), but the fit of the number and location of joinpoints will be heavily influenced by the larger cohort, unless an unweighted analysis is used. There is no "correct" answer, but careful consideration should be given to the overall purpose of the analysis in these situations.
For more details about the comparability or pairwise differences test, see:
http://surveillance.cancer.gov/joinpoint/comparabilitytest.html.