Eska is not "weird", not really. Her personality goes far far beyond "quirky". Wether the writers were aware of it or not, they wrote a character that showed clear, extreme, signs of genuine developmental disorders and asocialization.
This is a sad thing. This is tragic. This is a sick young woman who needs help.
This is Not Funny.
Bolin, circa season one, was sweet, considerate, honest, a little naiive, but thats really the worst thing you could say about the guy. I really liked Bolin, I thought Mako could go straight to hell and Korra could go suck eggs, but Bolin, I liked.
He was literally the perfect match for someone like Eska. To brute force their horrible subplot, the writers had to turn Bolin into an inconstant, inconsiderate, intolerable, cowardly dickhead.
A lot of people make a big point of how Eska treats Bolin. She's super controlling, but notice the way Bolin reacts to her. Theres no escalation or argument, she says something scary and he immediately pretends he thinks its a great idea. People with certain social disorders typically have an extremely poor grasp of boundaries, and a lot of "inappropriate" behavior comes from others never -setting- strong boundaries. I'm not saying mentally ill people cant be jerks, but Eska isn't.
What happens the -one- time Bolin actually talks back to Eska, actually stands up to her?
She listens to every word he says, lets him express his thoughts, and then pulled a complete heel face turn to accommodate him.
Eska's possessiveness is textbook overcompensation for a lack of confidence, or a lack of understanding, about the relationship. She doesn't understand why Bolin likes her, she outright questions the situation when he first approaches her. She clearly values the affection Bolin gives her, and that value combined with the confusion as to why leads to a certain kind of fear, here expressed by extremely controlling behavior due to her lack of boundaries. Look at Azula, and how controlling she was of her friends, that was all out of fear, fear that they would leave, that they would suddenly not love her. The cruel irony of Azula's character was that she surrounded herself with people who didn't need to be forced to care about her, and the more she tried to claw people closer to herself (as her level of stress increased) the more she drove them away, the more panicked she became.
Eska's behavior is certainly explainable by the fact that Unalaq shows neither of his children even the slightest affection, and from their speech and mannerisms it doesn't look like they've been in any normal contact with other people outside an extremely small group. When a young person's first instinct when approached by someone of their age they don't know is to growl at them, or talk about them in the third person to someone they know, you sail clear past practical examples and into theoretical levels of neglect. The twins behavior is on the level of feral children in terms of socialization.
While we're only given like, a few minutes of material in the show, Eska must have been extremely intimidated by Korra. Now, this isnt a physical intimidation, Desna and Eska from all accounts are fairly unmoved and unshakable when faced with physical violence (which might... suggest uncomfortable things about their upbringing). I tend to stay away from freudian ideas, but for lack of a better term, Korra presents a tremendous sexual threat to Eska's self image. Korra, from Eska's perspective, easily navigates social situations, has a publicly affectionate relationship, and most importantly, is dominant over Bolin in their social dynamic. Korra "controls" bolin in a way Eska -cant-, Korra commands his respect in a way that she can't, and has his affection (as platonic as it is, though such a thing would not be apparent to her) in ways that she does not. In very simple, cave man terms, Eska tries really hard and Bolin nervously whimpers, Korra does -nothing- and Bolin runs to embrace her.
Korra, not as a person but as an image in Eska's mental sphere, is so much that Eska herself is -not-, or would likely perceive herself not to be . She speaks "normally", she's tall and physically developed and indeed seems fairly confident about her body, men her age find her attractive and pursue her, she's a celebrity athlete and the most important figure in (for lack of a better term) the religion that has dominated every part of Eska's life and upbringing. She even gets approval and affection from Eska's father. She's got Mako, she's got Bolin, she's got loving, doting parents, she's got fans, devotees, teachers and friends who love her, she's even got Unalaq's attention. For Eska to perceive her as a (again, for lack of a better term) sexual/social threat, which would be very easy, would create a situation of extreme psychological distress in a uniquely vulnerable moment.
In layman's terms, she has inadvertently opened herself up to a very sensitive situation, come slightly out of her enormous, icy shell, and suddenly someone who represents in every way her inadequacies has completely destroyed that small bright spot that coaxed her out into the open.
It is unsurprising that she, when faced with the out of context problem that is Korra's social interaction, tries to force the conflict into a context where she is the confident one; physical violence.
Eska needs someone who will be very kind and loyal, but also clear and honest about what makes them uncomfortable. That should have been Bolin.