So how much stronger do the special equips get at higher level ups?
I've done Crane's puncher up to level 4, which doesn't seem to be worth it very much:
0: 1/80/50 (atk/stun/acc)
1: 1/86/50
2: 3/87/50
3: 5/80/58
4: 3/80/50, but also 6 res and 6 crit.
What we can learn from this is that every level is rolled from scratch, that is, something gained on an earlier level isn't bound to stick. It's just the amount of bonus that increases in total, and then that gets randomly distributed. Some bonus categories are fixed and do have a minimum/initial value, others are mere random bonus.
I've also done Lia's whip, up to level 9. And that was totally worth it, for atk increases steadily and about linearly:
1: 100/50 (atk/acc)
...
3: 300/60, but also 10 stun and talent
...
8: 1170/58, and 8 stun, 8 crit
9: 1260/55, and 15 crit and talent
Those 1260 attack are gonna whip some serious ass. And if you don't roll talent on level 9, you probably can just donate it again, and get another level 9 back, maybe this time with talent, or talent R even?
But honestly, it's kind of braindead to reroll this over and over again until you're happy. Might as well just cheat or something.