How to convert CO2 ppm volume to ppm weight?
You can't determine the concentration of CO2 in the water just from measuring the concentration in the air above the water.  

The solubility of CO2 is extremely dependent upon pH. See: http://ion.chem.usu.edu/~sbialkow/Classes/3650/CO2%20Solubility/DissolvedCO2.html

There is no indication you are considering pH at all.  

Solubility of CO2 also depends upon temperature.  

Also, you need to consider whether or not the phases are in equilibrium.