In this situation, you might do just as well to use a U-tube manometer. Is some respects, this is a sort of dead-weight tester where the fluid itself is the dead weight. In this device pressure is determined from the difference in height between two connected volumes of fluid. Usually this is just a transparent tube bent into a 'U' shape, placed upright in front of a convenient means of measuring the relative heights of the free surfaces of the liquid.
One end of the tube is connected to the pressurized volume, while the other is left open. The pressure difference may be calculated from the height difference.
$$ P = \rho g h $$
Where $\rho$ is the density of the liquid ($\sim 1000 \, kg/m^3$ for water) and $g$ is gravitational acceleration ($9.81 \, m/s$ in most places). Or, if you need your measurements in cm of water, simply use water as the working fluid and the height difference will be exactly the quantity you want. This is basically why "length units of liquid" can be used as a unit of pressure*.
If a standard manometer is not sensitive enough, you can tilt it off of vertical by some known angle. As a result, the liquid will travel a larger, more easily measured, distance along the tubes to achieve the same difference in height.
Despite the seemingly primitive technology involved, measurements of this kind can be quite accurate when performed correctly. There's a nice document from NIST that goes into detail about how to maximize the accuracy of these devices. Also a review by Ruthberg specifically for low pressure measurements.
*I don't mean to endorse these units of pressure. The pascal ($Pa$ or $N/m^2$) is the correct SI unit of pressure derived from the newton and the meter.