I ran simulations, using the Sour PR (Peng Robinson) and Sour SRK (Soave Redlich Kwong) equations of state. (Standard simulations used by chemical engineers to predict CO2 and H2S removal)
Assumptions : Temperature is 75F and Pressure is 55 psig (Reference : Sowell, Jeff. Consumer Affairs Specialist. Coca-Cola Company. Letter. 31 May 2000. cite )
Water and CO2 are pure - No other gases present
Results (Under the assumed conditions and purity - and with numerical approx) :
Mole percent of CO2 dissolved = 0.0029
1> Density of Water = 62.95 lb/ft3 or 1008 g/l (So the 2l bottle contents weigh 2016 g)
2> Density of Water saturated with CO2 = 63.02 lb/ft3 (So the 2l bottle contents weigh 2018 g)
Swapping N2 for CO2 for the same conditions above
Mole percent of N2 dissolved : 0.0001
1> Density of Water = 62.9452 lb/ft3 or 1008.2872 g/l
2> Density of Water saturated with N2 = 62.9428 lb/ft3 or 1008.2491 g/l