Let's say that I'm a Breton with 50% magic resistance. I'm also wearing a mundane ring, which further increases my magic resistance to 100%. Now, my birthsign is The Apprentice, which incurs a 100% weakness to magic.

Do my innate resistance and innate weakness cancel each other out, or does something else happen?

Not an expert at the mechanics, but I′d say you have no weakness or resistence as everything eliminates each other.

Hm. I was hoping one would take priority over the other. Like with Absorb, Reflect and Resist.