It's probably not too surprising, given that the novel calls him "Captain Blifil," that this guy used to be in the army. But it says something about his character that he keeps going by the title "captain" even though he has officially paid to get out of the army following a squabble with his superior, a colonel. He's a vain, cold, manipulative guy who will use anything he can to his own advantage, even an army title that doesn't really fit him any longer.
Like Mr. Thwackum a bit later on in the book, Captain Blifil reads the Bible a lot. But he never profits from its lessons about kindness and mercy. Instead, he uses most of his religious knowledge in vicious fights with his wife Bridget formerly-Allworthy, as the two of them violently disagree about Biblical interpretation.
Captain Blifil married Bridget because her children will inherit Squire Allworthy's pots of money. In fact, he thinks of his wedding as a bond to "Squire Allworthy's lands and tenements" (2.7.8), with Bridget as an incidental addition.
Once Captain Blifil has the marriage license in his hand, he immediately starts treating his wife coldly and patronizingly. He hates women (though he likes sex with them) and he despises his wife for thinking that she can argue with him about Bible study. In short, Captain Blifil is one of the nastiest pieces of work in this whole novel, and considering some of the awful characters in this book, that's saying something.
Captain Blifil spends most of his married life on his own, dreaming of the day when Squire Allworthy dies. He is so totally focused on inheriting Squire Allworthy's cash that an obvious obstacle never occurs to him: what if the captain dies first? In fact, as Captain Blifil is walking along one day and thinking about the squire's money, he falls over with a sudden stroke.
Captain Blifil's death is not only ironic (since he spends all of his time hoping another man will die, only to pass away suddenly on his own) but it also gives the narrator an opportunity to remind us that we can't count on anything in this mortal life. Not to get too philosophical, but there are always unintended accidents that can ruin even the happiest of plans. Squire Allworthy thinks so hard about the future that he forgets to enjoy the present. He's an awful guy. But even so, we feel bad for him, since he made himself so unhappy for nothing.
AP Biology teaches us that children inherit genetic traits from their parents. But even before people knew that these traits go from one generation to the next through DNA, RNA, and all that jazz, Fielding still suggests the importance of biological inheritance in his portrayals of his characters. So, Captain Blifil is a vain, greedy, proud, hypocritical guy. And even though he dies while his son is still an infant, Master Blifil shares a lot of his father's worst character traits.
By contrast, Mrs. Waters describes Tom's biological father, Mr. Summer, as "the handsomest person [she] ever saw, he was so genteel and had so much wit and good breeding" (18.7.2). Mr. Summer sounds a lot like Fielding's descriptions of Tom, even though, since he dies before Tom is born, Mr. Summer has had no direct personal influence on Tom's upbringing.