1) You don't need to actually re-sample the dataset, it is enough to just weigh the datapoints in the training of the classifier, i.e., the objective function of the weak classifier should be weighted.
If the sizes of the datasets are large enough, you can probably also use sampling and the size of the dataset you sample doesn't matter per se.
2) If you do use sampling and get redundant copies, you definitely should keep them as otherwise your objective function for the weak classifier will not be correct.