This axe seems to me useless for any job apart from BST. You are better off getting the Martial Axe, it's same damage/delay and 2 levels earlier, and is similar price on most servers, plus if you mainhand it you get the TP Bonus thing, which no one can complain about =)
with pet food zeta this axe was boosting the HP bonus of reward by about 9%. tested in boyohda with easy/even pets (as 75 bst). without the axe, Reward gave 410... with the axe Reward gave 447. tried it on both easy prey pets and even match pets and got 447 each time so i think its safe to say this is not a percentage boost based on pet HP.
also tried dual-wielding the axe but it didnt affect amount of HP restored. however there was a small difference. i'm a little tipsy and i can't type them out so i'll make a list:
BST75/WHM37 no axe: reward gives 410hp BST75/NIN37 no axe: reward gives 411hp BST75/WHM37 one axe: reward gives 447hp BST75/NIN37 2 axes: reward gives 448hp
so obviously the subjob is affecting Reward there. i haven't read up on Reward so this is probably not anything new. just thought i'd post it.
anywho this axe obviously boosts the HP gained from Reward. whether or not it enhances the Regen effect I cannot say. either way i'm keeping this axe... if bst is not your main job and you dont want to put millions in an axe, this weapon has a very good dmg/delay combo, and the 9% to Reward is a nice boost.
i rarely get to use my BST so i've just been using Francisca (sold my Wrath Taber after several years of amazing service.../sigh)... but this beauty is my new main. and quite a steal at 40-70k too (on leviathan atm).