Although Nightwing is one of the most popular Bat-Family members right below Batman, he might be able to grow in popularity if the Dark Knight stopped stealing his villains. Many people consider the Court of Owls to be Batman-centric villains, and it'd be hard to blame them considering how they've been used in stories lately, but the Court has always had a much stronger tie to Nightwing.
The Court of Owls first appeared in the New 52 canon of DC Comics where they were a painful thorn in Batman's side. They are a secret society that ran Gotham through the shadows for centuries, even taking up residence and hiding their bases in buildings owned by Wayne Enterprises. This eventually culminated in the Night of the Owls storyline, which saw a full-on attack from the Court on the Bat-Family and many people in Gotham, such as James Gordon. All of this sounds like they would make a perfect villain for Bruce, but over the course of the story, readers learn that they have such a stronger connection to Nightwing.
In Batman #7 by Scott Snyder and Greg Capullo, it's shown that Nightwing was originally meant to be one of the Court of Owls' enforcers, known as a Talon. He learns this when Batman so helpfully shows him that he has a Court of Owls engraving on one of his back teeth. But that's only the start of the personal connections. The entire reason Nightwing has this engraving is that it was presumably given to him when he was a child, living at Haly's Circus, which the Court of Owls had a hand in. The Court would pick the best acrobats from Haly's Circus and train them to be Talons, with Dick Grayson being only one of the many selected.
Nightwing is in need of his own rogues' gallery. He has a few villains here and there—Blockbuster, Lady Vic, Brutale, to name a few—but he still struggles to really find a strong stable of enemies that his adopted father Batman has. Even his archrival, Deathstroke, is considered by many to still be a Batman villain. The Court of Owls has had a much larger impact on Nightwing's life. Dick's great-grandfather, William Cobb joined the Court originally and was one of the reasons Nightwing was lined up to become a Talon. Since Dick was adopted by Bruce Wayne before he could be snatched up by the Court of Owls, they instead chose another young boy, one of Nightwing's best childhood friends, Raymond McCreary. Raymond wasn't as good of an acrobat as Nightwing though and despite the brutal training he underwent, he was eventually refused entry to the Court and abandoned on the streets.
Batman has a strong roster villains, some of the best in comic history, and all of them relate to him in some way. Joker pushes his moral code, Riddler challenges his intellect, and Two-Face reflects the duality of his identities. Nightwing does not really have many villains who are related to him in any such way. Blockbuster is simply some mafia boss who lives in the same city as Nightwing. Lady Vic is an assassin and there isn't much relation between them. The Court of Owls, however, has as big of a personal connection to Nightwing as anyone ever could, which is why they were always his villains and not Batman's.