Don't know the exact size of the nuts, but do know you need two short handle wrenches to get in there. I've used a plumber's pipe wrench before and it will work. You need to back off the lock nut, and tighten the shaft nut just a bit, then re- tighten the lock nut, while holding the shaft nut from turning.
It should not drip while not spinning, and drip 6-10 drops per min. while in gear.