Which airports consume the most fuel for aircraft refueling, and how much fuel do they use? I was able to find that "Heathrow uses about 20m litres of fuel a day", but it isn't easy to find figures for other airports.
The best data I could find is in this paper about biofuels, which has data for US airports in 2014. Based on my reading of the chart on page 14 and some conversion:
Airport Millions of barrels per year
Comparing this to the top US airports in 2013, it is interesting to note that LAX and JFK use significantly more fuel than KATL, despite passenger traffic figures ranked the other way. Also notable is Anchorage showing up here right after DFW, while MIA and ANC are the only ones not in the top 10 by passengers, showing up at 11th and 58th, respectively.
Figures for other countries have been harder to find. This article from 2004 estimates the Dubai International usage at 24.2 million barrels that year, which has certainly grown since then. The 2012-2013 environmental report from Emirates Group lists their consumption at 73.9 million barrels, and half of this figure would be in line with the other numbers available.
I found a similar figure for Heathrow, listing it at 20-25 million liters per day, depending on season, which gives a range of 61.2 to 76.5 million barrels per year, well ahead of the US airports.
Becoming even fuzzier, the pipeline to Narita Airport in Tokyo transported 130 billion liters in its first 30 years of operation, which averages out to 36.3 million barrels per year.
I found a few sources of data that is close but not specifically what you are looking for (Im going to keep looking)
Here is the total Jet fuel consumption reported by the DOT (you can filter by airline/carrier)
Here is the Jet fuel consumption by state in the USA
Here is an interesting report on fuel storage at airports.
Im sure the number vary over time as well as seasonly depending on where in the world you are talking about. On one hand you can argue that the distance/weight comparison of airports may be a useful metric. If we assume planes are least efficient and require the most fuel when flying far and heavy the airport with the greatest departing mass/distance value could shed some light on the number you are looking for (I have no idea how to figure out that number for the record).
Keep in mind that there is a growing number of planes that are running on Jet A1. A solid chunk of the smaller charter fleet that runs Turbo Props runs on Jet A1 as well as planes like the Piper Meridian and other similar turbo props sneaking their way into the GA market. To round it out diesel GA planes run on Jet-A1 and things like the Diamond-DA42 are making an impact on the GA market and increasing Jet-A1 consumption even if just marginally. That all being said just because a state has a single large or even mega sized airport other states with lots of GA or small charter traffic out of little fields may be able to keep up.