Location: The Hideaway (ship)
Petitioner: Dorys
Unlocked: Complete Getting to Work
Reward: The Breath of Fire (Rising Flames), 40 Sharp Fangs, 40 Steelsilk, 15 Renown
To trigger this side quest you need to complete the quest Getting to Work, which is a sub-quest of the main story quest Bolts from the Blue. Both are fairly simple quests to finish off, and you won't need to complete Bolts from the Blue in its entirety to make The Weight of Command appear.
The petitioner for this quest, Dorys, is standing on the walkway next to the Board Deck of the Hideaway. Speak to her and she'll tell you that a team of Cursebreakers has gone missing. Apparently they were trying to free Bearers, but the mission was interrupted by goblins. Dorys wants Clive to look into the matter, though she can only tell him that they're somewhere near the Dragon's Aery.
Jump to either the Northreach Obelisk or the Dragon's Aery Obelisk. The next quest marker is between the two Obelisks, in the Dragon's Aery and along a dirt path. Arrive in the area and you'll find the Cursebreakers tending to some Bearers. Speak to Cole, the leader, and you'll learn that some of the Bearers are still locked away in a nearby carriage.
Turn south and you'll see the carriage. Trek over to find several Goblin Leechers and a Gigas Bruiser waiting outside the carriage. Despite the names they're all just normal Goblin and Gigas enemies, and shouldn't pose a massive threat - especially if you rush the magic-using Leechers first and wipe them out. The Gigas is easy to Parry with Limit Breaks.
You'll receive a Bone Necklace and Magicked Ash for defeating the beastmen. Head back to Dorys at the Hideaway after the fight - she has relocated to the Mess - to receive your reward.