To be clear, the centripetal acceleration is equal to the tension on the string, the tension in the string is equal to the force due to the gravity on the hanging weight.
Does a mass of 0.1945 kg or 194.5 g for the rubber stopper makes sense? Which implies it is as massive as the weight.
I assume you know the value of the weight you used that is at the end of the string. The radial force, is of course, equal to this weight ##w##. So you can write $$r = \frac{w}{4\pi^2 m} T^2$$. The slope you calculated is equal to ##\frac{w}{4\pi^2 m}## where you can get the mass you're looking for.