[rabbit73]

If you did aim the antenna at 347 and you see a difference with a small change in height, then it is probably due to a roof reflection which can help or hinder the direct signal.

The path for the reflected signal is longer than the path for the direct signal. When you change the height, you change the path length of the reflected signal so that it arrives at the antenna at a different time, which changes the phase relationship of the two signals.