Last winter the finish on the bottom my Wherry (Interlux) was discolored where the poly tarp came in contact with the paint.  There doesn't seem to be a problem with paint-to-wood adheasion, just looks bad.  The boat is getting repainted this winter and I will avoid plastic to paint contact in the future.

I store mine under the eaves with a tarp covering it where the Yak sticks out, the yak is wider than the eaves. I have had to replace the cheap tarp about every two years.

I would suggest proping the tarp up off of the boat, maybe as simple as a couple of boards across the boat with the tarp drapped over.

Mine spent all winter under a blue tarp and the only issue I've had were tarp marks in the paint on the bow (probably from before the paint had cured enough).

Mihai