I think Rocks was betrayed by most of his crew at God Valley, which made Blackbeard decide to get revenge on those involved with God Valley or their descendants:
1.Capturing Ace, who turned out to be son of Roger and illegitimate son of WB.
2.Told Luffy he was looking for him before he ran into Ace (Grandsons of Garp the Hero)
3.Crewmate of the former first mate of the Rocks pirates, Whitebeard. Sailed under him for decades, then killed him at Marineford to take his devil fruit.
4.Captured the Hero of God Valley, Garp
5.Placed a permanent scar on Shanks' face (the cabin boy of Roger and son of Figarland Garling, both present at God Valley)
6.Invaded Amazon Lily for Hancock's power (unsuccessful,) knowing this is where Gloriosa is from.
7.Attacked Thriller Bark because of the shadow corpses of the Rocks pirates
8.Assaulted the original RA base (Dragon, son of Garp the Hero).
9.Made Catarina Devon copy Saturns DNA (Saturn was on God Valley, subservient to IMU)
10. He kidnapped Pudding.