Skepticism equals not placing bets. Not placing bets demonstrates low confidence in your beliefs. Abstaining from bets exercises your skepticism. Your skepticism goes up when you don't place large bets and then you consequently don't lose.

You can also exercise skepticism by betting against something. E.g. if a scientist puts their reputation on the line to say that some well regarded theory is incorrect, they are simultaneously skeptical and have high conviction. I'd guess in human experience skepticism appears alongside the expectation of negative value outcomes while conviction has to do with positive expected value.

When you discover you have been wrong, your priors weaken. When you discover you have been right, your priors strengthen.

Somehow this is incorrect. More true to say that when you get evidence consistent with your hypothesis your posteriors have higher confidence. That's not changing your priors, unless you're talking about the priors for the next round of inference.

How does one know when and on what to apply her conviction/skepticism? Any general heuristic/strategy?
By the survival value and urgency/importance of the favored result of what one is doing at the moment?

Thanks!