Actually, those are a sign of a generally healthy forest - it means there is lots of groceries at the lower end of the food chain, which is where the rubber meets the road in the biodiversity sense.
Most members of the weasel family are quite innocuous and friendly. We once had a mink who moved into our trap line cabin and had her litter under the floor boards; she came up three or four times a day to mooch food, which she'd take from your hand. Damn thing was crazy for cheese. You had to keep the cheese locked away, or she'd dig it out and steal it all!
We also had a tame weasel (in an old farmhouse that I once lived in) who'd climb up on the screen door and chirp like hell, demanding to be let in - and who'd then head straight for the fridge, and raise more hell until it got fed! In neither case was any effort made to tame them; they just came around and 'tamed' themselves. Both were utterly clean; never as much as a 'squirt' of weasel stench or any droppings anywhere. As far as I was concerned, they earned their keep by keeping the mice down. They make a cat look like an amateur, as far as mousing goes.
All in all, I wouldn't worry about a marten climbing 'my' tree - I'd just chalk it up to another great outdoors experience.
I would imagine wolverines might be a bit less friendly...*L*..I'd be more nervous if one of them climbed my tree.