Small tertiary airports often served by short regional flights don't have a lot of infrastructure. They have a couple of fuel trucks and a gate agent/security screener/baggage handler who might all be the same person.
So instead of a fuel truck you have a battery swapper.
You'll have to ship the batteries somewhere they can charge/reprocess, but you also need to ship fuel, so it's a 1-to-1 tradeoff (you can ship the batteries by land).
Not that much more (theoretically) - Al-air batteries could reach up to ~8kWh/kg, which is in the same range as jet fuel's 12ish. Aluminum is also denser than jet fuel, so per unit volume it could be even closer.
You'll have to ship the batteries somewhere they can charge/reprocess, but you also need to ship fuel, so it's a 1-to-1 tradeoff (you can ship the batteries by land).