I have tried to simulate the program with the proportional band at 200%, this is my results:
error output
0% 0%
50% 25%
100% 50%
101% 100%
With this setup I will never get the jump in output because the error will never bee 101%, but 200% proportional band is too slow for the process and the regulation will not work.
Here is a image form the documentation showing how the output of the proportional band should work and how mine is working. The red line is how it should work, mine works like the green line, which I have added to the image.