OK, just to be contrary, I'll say this:
A. I can't see why any well-designed hardware (like the Davis stuff) would transmit "weird wind readings", just because it wasn't grounded. It's wireless, and RF doesn't care about grounding. [If I'm wrong, then you'll find out soon enough about weird readings]
B. If you ground the tripod and mast, and it gets struck by lightning, your Davis stuff is toast. So, grounding isn't going to help that part.
C. It looks like there are a lot of other "targets" around you. And the trees are probably taller?
D. Does your homeowners' insurance care?
I think you've got the "increased risk calculation" about right.