The way I think it should go is if your prestige exceeds the value that you should have when you just do the missions themselves, you should be able to unlock the upper Weapon Rank and Tier.

Personally, I'm getting bored sitting here with my unheated 4* equipment that I "grandfather'd" through the rank locks. I'm keeping myself at Knight rank because I enjoy derping around with new players. I have 12k prestige OOO pls.

side note: dual damage Avenger outscales Khorovod in neutral damage (seen with damage orb buff), even when the Avenger is just level two and the Khorovod is level ten. ;m; so bizzare