In commercial aviation (passenger/cargo), typically about half the take-off weight is fuel. That's not half the payload weight (pax + cargo + fuel), it's half the takeoff weight.
For a medium-range flight (say ~2000 mi / 3200 km) each passenger incurs somewhat more than their own weight in fuel.
I don't think that's correct. The MTOW (Maximum Take-Off Weight) of an A320ceo is 78,000 kg, while the max fuel capacity is approximately 24,210 litres. Using Jet A-1's density of roughly 0.804 kg/L, that's about 19,460 kg of fuel, which represents only 25% of the take-off weight. The OEW (Operating Empty Weight) for that aircraft is approximately 42,600 kg, which means you'd need the fuel to weigh around 35,400 kg for your "half the take-off weight is fuel" claim to be true—nearly double the actual fuel capacity.
Even for a long-range aircraft like the A350-900, with an MTOW of 280,000 kg and a fuel capacity of approximately 138,000 litres (roughly 111,000 kg at 0.804 kg/L), fuel represents about 40% of the take-off weight. The OEW is approximately 155,000 kg, meaning even a completely empty plane (except for crew) loaded with maximum fuel still wouldn't reach your claimed 50% fuel fraction.