Allocating People into Groups with SQL the Sequel

In our prior story about allocating people with the power of window aggregation, we saw our valiant hero and heroine trying to sort people into elevators to ensure that each elevator ride was not over capacity. All was good in the world until someone named Frank came along and spoiled the party. Frank rightfully pointed out that our algorithm was flawed because should Charlie double his weight, then we could have one elevator ride over capacity. We have a plan.