Why, given Sonya's condition, has Hank taken her under his wing? The kindly performance given by Ted Levine as Hank explained only so much - he's a good cop in an administrative position, after all, and although Sonya is also a good cop, an excellent cop in many ways, she's also always on the verge of saying something that could throw a case off course, or shut down an otherwise talkative suspect. So why does Hank not only put up with her, but allow her to be a leading investigator on a crucial case?
It's because, as Hank explains to Marco, he years ago shot the rapist and killer of Sonya's sister in the head, rather than taking him into custody, and the bullet left the killer alive but unable to communicate. This created a situation of maximum frustration for Sonya, in which her sister's killer continues to be just beyond her reach and ability to find out any answers about her sister's killing. Rather than the cold closure of her sister's murder, Sonya has been left with an open wound, thanks to Hank.
And there's something else about Hank, which I don't really think is the case, but my wife brought up as we watched the end-of-Gina scene - after she bolts from the bar - so I'll put out here anyway. With Sonya and Hank running after Gina separately, that leaves open the long possibility that maybe Hank shot Gina. Now, I can't recall every seen in which we've heard from the killer in The Bridge so far, and exactly where Hank was at all of those times, or the expression on his face every time the killer comes to his attention - which is most of the time - but I would say there is an ever so slight possibility that, though Hank is not the killer, he is working with rather than against the killer in some way, and towards that end killed Gina. And, if you want to be really diabolical about it, you could reason that Hank put Sonya on the case so that he could better control its outcome (to cover up his involvement) or even in the expectation that she would wreck the case.
Nah - I don't think I believe that - but the very fact that it could be a long-shot option shows what a complex, excellent, mind-bender of a story The Bridge is giving us.
See also The Bridge Opens Brooding and Valent ... The Bridge 1.2: A Tale of Two Beds