What does one liter of CO2 weigh?

0.0013g -- For dry air at STP which is 0C (273.15K) and 1 bar (100 kilopascals or 1 atmosphere))

Improved:

Air Weights can very at different temperatures and sea levels.

With different temperatures or pressure, the density of air is:

d = p/(R x T)

d is the calculated density of air (g/cm^3)

p is the pressure (kp or kilopascals)

R is the specific gas constant -- 287.05 Joules/(kg*K)

T is the Temperature (K or Kelvin)

With different altitudes and any water vapor (humidity), the weight of air varies in a much more complex fashion.