Is there a way to calculate counterweight for the pressure relief damper required for staircase pressurization where 50 Pa is to be maintained?

I never face problem like that because this is not always constant and change as per site conditions but its simple

pressure = force/area

Pressure you need is50 Pascal

Now calculate the flow as per the staircase volume and get the duct size and then you will get the area of the damper as well so as per the gauge you will find the weight of the dampler

P = F/A

P * A = F F = force and here force will be same as weight to counter that pressure

Hope this will work

No,but you can adjust the used weight on the pressure relief damper  to match the required pressure that has to be maintained in the stair case which is50 Pa

actually i did not face this problem befor but i think there is a simple solution by applying mechanical force balance as below :

P=M * g * A  which;

p = pressure in pa

M = mass in KG

g =9.81 m/s2

A = cross sectional area for the damper

for example :

50 = M *9.81 *1

M =5.1 Kg 

put i think there is another factor for the moment arm wich will decrease this mass and we will chose less mass according to the arm length