Edit with updated information:
So I purchased 3 CNJ weapons today: the rank 1 Weathered Cane, the rank 6 Ash Cane, and the rank 11 Elm Cane, with the intention of testing out how the "optimal rank" affects your weapons and the stat scaling.
While my sample was obviously very limited so far, my initial conclusion at CNJ rank 6 were that:
Any weapon higher than your current rank acts as a rank 1 weapon of the appropriate type until you hit its optimal rank, after which it grants the additional stats.
For example:
CNJ1 to CNJ5: All three weapons acted as a Weathered Cane with no difference in stats or damage.
CNJ6: Weathered Cane continued to be a Weathered Cane (shock horror!), but the Ash Cane unlocked allowing its improved stats. The Elm Cane remained the same as the Weathered Cane.
CNJ7: Weathered Cane continued to be a Weathered Cane, Ash Cane remained an Ash Cane, but the Elm Cane gained +2 to Magic Potency, Magic Accuracy, and Magic Defense over the Weathered Cane. (Interesting!)
CNJ8: Elm Cane gained another +2 to Magic Potency, Magic Accuracy, and Magic Defense. Still Below the Ash Cane, however.
CNJ9: Elm Cane gained another +2 to the same stats. Still below the Ash Cane. Optimal rank for Elm Cane is 11, so I can't see it catching up before I hit 11 and its stats shoot up.
CNJ10: Same story. +2 more points to the same stats.
EDIT: That mostly concludes my testing for the day. It seems that the following conclusions can be drawn:
1) It is ALWAYS better to use equipment that you have hit the Optimal Rank for. (eg. If you are a CNJ 10, it is always better to equip the Ash Cane (optimal 6) than the Elm Cane (optimal 11) if you have the choice.
2) If you don't have the choice, a higher rank weapon will always be at least as good as the rank 1 weapon, and while it will get better over time, it will still fall short of optimally ranked weapons inbetween.
Again, not conclusive, but I thought it was an interesting and worthwhile experiment.