How to convert CO2 ppm volume to ppm weight? I'm using a sensor that measures $\ce{CO2}$ in ppm by volume aka atmosphere.
What I'm using it for is to measure $\ce{CO2}$ concentration in water which is measured in ppm by weight.

This is what I have so far

$$\text{Ppmwco2} = \text{ppmvco2} \times 0.8317 \times 44.01 / 10000;$$

This is quicker than $\text{co2}/1000000 \times 0.8317 \times 44.01 / 1000000$. 0.8317 accounts for Henry's Law and max ppmw will be 36.6 with 10,000 ppmv.

The sensor floats on the waterline detecting any $\ce{CO2}$ bouncing out of the water. Do I even need to account for Henry's law? Is the math right?
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.