  Comparing concentration properties of uniform sampling with and without
replacement has a long history which can be traced back to the pioneer work of
Hoeffding (1963). The goal of this short note is to extend this comparison to
the case of non-uniform weights, using a coupling between the two samples. When
the items' weights are arranged in the same order as their values, we show that
the induced coupling for the cumulative values is a submartingale coupling. As
a consequence, the powerful Chernoff-type upper-tail estimates known for
sampling with replacement automatically transfer to the case of sampling
without replacement. For general weights, we use the same coupling to establish
a sub-Gaussian concentration inequality. We also construct another martingale
coupling which allows us to answer a question raised by Luh and Pippenger
(2014) on sampling in Polya urns with different replacement numbers.
