] ...why in the world does he love her?? We've all been pretty hard on Marianne this read (with reason, I believe), but why would such a wonderful, sweet man like Col. Brandon fall in love with such a whiny, petulant, selfish brat like Marianne? I suppose some men like that in a woman, but.... And especially after she continues to treat him with rudeness and disdain.
Simply because love is irrational. If we put aside the fact, that she reminds him of the past, this is a big part of the answer IMO.
When one is in love, one most often doesn't choose the most suitable partner. I cannot imagine a person in love thinking: "He/she is so mature and suitable - that's why I love him/ her". :-) One simply loves.
If the desired object doesn't return one's feelings, or even worse, treats them contemptuously, illusions and hopes begin to console and wilfully blind the lovesick person. Besides, one is always prone to tolerate bad behaviour from loved ones.
When I come to think what could have attracted the Colonel, it could be thus summarized: Marianne is intelligent, well-read, sensitive (not to other people unfortunately). Compare her to other young ladies like the Steele sisters (very vulgar)or to Mrs. Jennings' daughters (true, they are married, but were and are nevertheless very stupid). In such cases we must think of the available ladies to the Colonel. They all fall into the spiteful ones (true, Marianne is sometimes cruel but not to people beneath her and never relishes and wilfully manipulates because of her ill-will like Lucy Steele) and/ or the foolish ones (of course, Marianne says some pretty stupid things but her lack of experience and her youth excuse her to some extent; besides, she is not hopelessly stupid).
I think the Colonel is much attracted to two main principles: lack of mercenariness esp. in marital choices and dignity.
In a conversation with Edward Marianne professes that a family needs at least 2 000 pounds a year (Elinor is much more realistic and names half that sum). But Marianne falls for Willoughby, who is practically poor - his income and estate are small, he expects to inherit from Mrs. Smith, but when and whether this would happen is not very clear. So if Marianne was really mercenary like most of the other ladies around, she would have chosen the Colonel, because he is better financially than Willoughby (here I take into consideration only their financial state, not their respective qualities, that have contributed to its improvement or worsening - we know Willoughby is reckless and always spending more than he ought and the Colonel has paid all his brother's debts and is very careful with money). So in that respect the Colonel is a more attractive i.e. richer catch.
But Marianne prefers to follow her heart and for this she deserves respect. And that's why the Colonel respects her. He was bitterly hurt by mercenary and lacking in principle people in the past, so he admires everyone that sticks to his/ her ideals and principles (Marianne and later Edward) even and especially when it is clearly not in his/ her best interests to do so.
As far as dignity is concerned, Marianne never loses it. She may act imprudently and stupidly and lacks self-control but she never flatters her superiors (true, Marianne is generally not given to praising others, even when they deserve it) and never manipulates. IMO the Colonel is allergic to manipulation. Besides, she is always impulsively cruel but never deliberately cruel like Lucy. Lucy plans in advance what to say to disappoint and hurt Elinor the most, while Marianne avoids and hurts the Colonel and other people instinctively, without deliberation. She doesn't think several days in advance: "Let's find more intricate and effective ways to stab the heart of the old Colonel". He understands that and forgives her impulsiveness. But if she were deliberately cruel, the Colonel wouldn't have cast a second glance at her, I am sure. Having said this, I don't mean to justify her lack of politeness and self control. She often ignores good manners.
Besides I must add a third quality much prized by the Colonel: openness. In this respect he resembles dear Mr. Knightley :-) He was deeply hurt by insidious hypocrites in the past and cannot stand this sort of people (John Dashwood for example). And Marianne is VERY open. One would wish a bit of restraint on her part, because extreme openness borders on rudeness. Here Elinor is far behind her and this is her predicament - she cannot tell anyone about her sorrows, because of her promise. IMO the Colonel feels she is a bit distant and probably attached to someone else. This is one of the reasons, that he doesn't consider her as a partner.
The Colonel realizes that Marianne doesn't like him in spite of or maybe even because of his eligibility. Of course, this pains him, but he would have been much more pained if she had instantly shown interest in him. Let me exlpain myself: he knows he is not very much attractive to young ladies at first. Therefore if Marianne had shown interest in him soon after they were introduced to each other, she would have demonstrated hypocrisy and mercenariness. The Colonel would feel this very acutely. But then he wouldn't have fallen in love with her and would have probably despised her.
So to summarize: Colonel Brandon falls in love with Marianne, because one often doesn't choose one's object, because love leads one on. Besides Marianne best covers three very important requirements of his: she is not mercenary, she has dignity and she is open compared with all other young ladies around him. Since she answers his main criteria, he is ready to forgive her faults and rudeness, because in his opinion, they just confirm her good qualities and attractiveness.