Cats are not persons. 'Cept for Thundercats, of course.
Yeah, I agree with this. And at the time, Wesley felt himself to be a villainous character (being outcast by Angel et al, keeping a woman locked up in his closet, etc) and I think, much to his horror, he loved her quite deeply, too.
I think Angelus and Darla loved each other. Even when one left the other to be killed, they never held it against each other. Angel said he spent one hundred years looking for Darla, and it was clear that she was his obsession, even when souled. I know Angel and Buffy were supposed to have the Epic Love to End All Epic Love, but I think S2 and S3 of AtS demonstrate that even though there wasn’t anything good about Angel(us)/Darla, they loved each other.
There’s something of a sub-genre in the movies of the “rampaging couple in love” – Bonnie and Clyde, Kit and Holly in Badlands, Mickey and Mallory in Natural Born Killers. I suppose it’s subjective whether any of these protagonists qualify as “villains”, but they all commit barbarous acts.
True, but when Ivanova asks him why he didn’t get her out of the “re-education facility”, he answers, “Because I don’t have that kind of authority!”, meaning that he would have if he could.
He also describes his promise to take care of her as “the only promise I ever made that means a damn to me.”
Sounds like it fits the OP to me. 
In Kim Possible, Dr. Drakken and Shego are clearly attracted to each other, but don’t act on it for most of the series. I remember an episode in which Shego is taking a romance quiz in a magazine and asks Drakken a question from the quiz about what he’d do to get the attention of someone he likes, and he says something along the lines of, “I dunno, maybe use a mind-control device?” He had done exactly that to Shego in a previous episode. Also, he was acting rather jealous when Shego tutored Senor Senior Jr. on how to be evil.
Yeah, but doesn’t Sheego like Kim in at least three senses?
“Buffalo Bill” from Silence of the Lambs actually seemed to care about his dog.
Dogs aren’t peope. Except Underdog.
Only in fan fiction.
I didn’t mean sexually. But it’s clear that Sheego enjoys fighting with Kim for its own sake, and that she respects her skills generally, and I seem to recall Sheego losing her memory due to some plot contrivance or other and becoming friends with her quite quickly and easily.
Yeah, but really now, which would you count as being more of a “beast”—the tiny, fluffy, lovable little dog; or the guy who kidnaps and kills people to sew their skin into clothing? 
I gotta figure that, once you’ve got all the factors tabulated, those two actually come out about even on the “basic humanity” scale.
Based on the series as a whole Snape is not a villain. Certainly not a hero, or an unambiguously ‘good’ man, but not a villain.
Bellatrix hearts Voldermort?
Well, he loves Dawn. He really likes Joyce.
But Spike hates Angelus and Angel. Angelus is such a cocky, moronic, annoying vampire, Spike seems to wish he never existed. Angelus even tried to end the world, which makes no sense in Spike’s mind.
He might hate Angelus more than Angel, actually.
Oh, you mean his mother. You are right, of course. But he does like Joyce, too. 
Master & Blaster in “Mad Max Beyond Thunderdome”
Another one from Batman - R’as al Ghul and his daughter.
He doesn’t seem to care too much about Nyssa, and he’s currently at war with Talia (over his plans to take possession of her son’s body), so, I’m not really sure he counts.
Surely you jest. Ra’s became loveless at least half a dozen resurrections ago. I don’t think he even loved the Earth any more; he’s at least twice as evil as Lex Luthor.
I’ll be in ma’ bunk.
Ew.
Ew.
Ew ew ew ew EEEEEEEWWWWWWW.
Frank Burns loved Hotlips.