Yeah - literal step-by-step. (Controller directions)

1. Click the Character drop-down context menu (open menu, go to Character tab)
2. Click on the "Armoury Chest" option (scroll to the Armoury Chest option and press X)
3. In the Weapons Tab, find your Weathered Axe and open the Sub-Commands with right click. (Square on controller)
4. Press "Equip." Your Class should now change to Marauder, and the quest should be unlocked for you.
5. Talk to him again!
6. Level to 15!
7. ???
8. Profit.