The Histogram command has a built-in option where you can provide a column of weights, but the Box command does not have this. Perhaps it should, but for now would a weighted Histogram work for you?
If not, are the weights, integer values that provide the number of counts for each item? If so you could reconstruct the data using expressions, and then use the Box command on the reconstructed data. We could post an example if that is what you need.