I pulled the weapon skill upgrade chart from elsewhere (with some modifications), and it only listed an upgrade path for SR weapons. Now that I have an SSR weapon I'm filling it in as I go, but I've only filled it in up to LV3 at the moment. You'll need to enhance with 2x Rares (simultaneously) to get from Level 1 to 2, and then 4x R to get to LV3. The goal is to always have a 100% success rate with no wasted 'points'.

Upgrading SSR SKILL LV

1 to 2 2x R
2 to 3 4x R