Hey, guys,
Thanks all for the inputs.
On sunday, I checked again on the issue.
What I did is to loosen the support on the trailer and make the boat free to roll a little bit on trailer.
What I found is that the boat is not weight distributed balance. It roll to the starboard side because it is a side console - boston whaler Newport 1970's. And this is why the tail of engine tends to turn to starboard.
When I managed to push the boat to port side on trailer, the problem is solved or not noticeable. When sitting still in water, I believe this will be the same issue.
I such case, I guess I have two options. 1. to balance the boat, 2. to replace a hydraulic steering system, which is expensive