Extra money added to someone's pay because living in that place costs more than average. In Britain this is very common: a job in London may pay a "London weighting" of a few thousand pounds a year on top of the normal salary, because rent and travel there cost so much more. The word is used mostly by employers, unions and job advertisements — you will see "salary £30,000 plus weighting" — and it sounds official rather than everyday. Note that the money is not a reward for working harder; it only balances out where you live. Americans usually say "cost-of-living adjustment" or "locality pay" instead, so this exact use of "weighting" may sound British to them. The same word has a wider, more common meaning too: giving one thing more importance than another when you count or measure. If a teacher says the final exam "has a weighting of 60%", she means it counts for more than the other tests. The pay meaning grew out of that one — you "weight" the salary up for an expensive city.