I found this study which suggests that the water vapour content of the atmosphere is increasing, but that increase is due to the warming of the atmosphere. Warmer air can hold more water vapour.
https://www-pls.llnl.gov/?url=science_and_technology-earth_sciences-moisture
External Quote:
"When you heat the planet, you increase the ability of the atmosphere to hold moisture," said Benjamin Santer, lead author from Lawrence Livermore National Laboratory's Program for Climate Modeling and Intercomparison. "The atmosphere's water vapor content has increased by about 0.41 kilograms per square meter (kg/m²) per decade since 1988, and natural variability in climate just can't explain this moisture change. The most plausible explanation is that it's due to the human-caused increase in greenhouse gases."
Kilograms per square metre seems like a rather strange unit, but I suppose it removes the effect of varying pressure (and therefore weight per unit volume) as you go higher into the air. So presumably this refers to the mass of water vapour in the atmosphere above each square metre of the Earth's surface.
The surface area of the Earth is about 509 million square kilometres, or 5.09 x 10
14 square metres.
So the total water vapour content has increased by 0.41 x 5.09 x 10
14 = 2.09 x 10
14 kg.
Taking the annual usage of jet fuel as 2 billion barrels, with one barrel being 42 gallons and one gallon weighing 6.8lb (or 3.08kg), the amount of fuel burnt in a decade is 10 x 2,000,000,000 x 42 x 3.08 = 2,587,200,000,000 kg, or 2.59 x 10
12 kg.
Each kilogram of jet fuel produces 1.37 kg of water when burnt, so the total "new" water from that jet fuel is
1.37 x 2.59 x 10
12 = 3.54 x 10
12 kg.
Dividing that by the increase in water vapour content we get:
3.54 x 10
12 / 5.09 x 10
14 = 0.017.
So jet fuel consumption in one decade has produced about 1.7% as much water as the increase in water vapour content due to warming.
Actually I was surprised it was as high as that.
Edit to add:
From this paper, the average total mass of water vapour in the atmosphere as a whole is 1.27 x 10
16 kg. The annual contribution from jet fuel combustion (3.54 x 10
11 per year, calculated above) is about 0.0028% of this amount.
http://acd.ucar.edu/~lsmith/massERA40JC.pdf