The hitch here, of course, was that, with whatever beauty, her sister, widowed and almost in want, with four bouncing children, was not a sensible value. (184.108.40.206)
Kate's poor sister Marian is basically toast as far as social mobility. For starters, she made a bad marriage to a guy who sounds like he was worthless—a surefire way to lower yourself on England's social ladder. But worse still, the dude up and died, taking away Marian's only source of income. Within the British class system, Marian basically has no value as a person. And if that sounds harsh, that's because it is.
"Ah, you naturally want to marry her to a duke, and are eager to smooth away any hitch." (220.127.116.11)
Merton might not always pick up on social cues, but he's no fool. He understands that Maud Lowder wants to marry her niece Kate to someone important or rich, and that she therefore wants him to stop courting her. But good ol' Mert has other ideas.
A less vulgarly, a less obviously purchasing or parading person she couldn't have imagined; but it was, all the same, the truth of truths that the girl couldn't get away from her wealth. (18.104.22.168)
Milly is very modest about her wealth—she's not doing the turn of the century equivalent of bathing in champagne or sticking her head out the sunroof of a limousine. But try as she might, Milly can never disguise the fact that she's filthy rich. It's just a part of who she is.
[His] early years abroad, his migratory parents, his Swiss schools, his German university, as she had easy attention for. (22.214.171.124)
Poverty is not the only reason that Maud Lowder has a problem with Merton Densher. She also doesn't consider him to be quite "English" enough to marry her niece, Kate. Merton is a tough guy to pin down, and part of this might because of his unconventional upbringing. He has spent many years traveling with his parents and spent his university years in Germany. People in James' time would have been a bit wary of people educated abroad because they wouldn't quite know how to judge them. And, at least according to upper-crust English social code, people that didn't fall into a clear class bracket were untrustworthy.
The idea of his frivolity had, no doubt, to do with his personal designation, which represented […] a connection with an historic patriciate, a class that, in turn, also confusedly, represented an affinity with a social element that she had never heard otherwise described than as "fashion." (126.96.36.199)
Milly can see that Lord Mark comes from a long line of important British people. The man himself isn't all that wealthy, but he has the type of breeding that can only come from hundreds of years of familial wealth. In other words, social class isn't just based on money; it also is based on history.
"Mr. Merton, she holds […] won't ever be either a public man or a rich man. If he were public she'd be willing, as I understand, to help him; if he were rich—without being anything else—she'd do her best to swallow him." (188.8.131.52).
It's not like Merton needs to be rich to marry Kate. Aunt Maud would be just as satisfied if he were somebody important, like a politician or lord. But because Maud is convinced he'll never be rich or important, she has no interest in having him marry Kate.
[Lord Mark] had interposed, taking the words out of the lady's mouth and not caring at all if the lady minded. That was clearly the right way to treat her—at least for him. (184.108.40.206)
Lord Mark quickly cuts off a woman when she tries to invite Milly to a party. Normally, it would be a pretty rude gesture. But Milly can tell from the woman's reaction that Lord Mark can treat her this way because he's high class.
[Susan] had high-lights as to the special allowances made for the class, and since she saw them, when young, as effete and overtutored, inevitably ironic and infinitely refined, one must take it for amusing if she inclined to an indulgence verily Byzantine. (220.127.116.11)
Susan doesn't care all that much for upper class snobs. But that doesn't mean she'll pass up a chance to be Milly's hanger-on. Susan is a proud and intelligent woman, and it's because she's proud that she seems determined to treat the much wealthier Milly as a sort of possession, using her age as a way to be a mother-figure to the girl.
You're an outsider, independent and standing by yourself; you're not hideously relative to tiers and tiers of others. (18.104.22.168)
Milly is very baffling for the people in London because they have no clue how to place her within their rigid class system. First of all, she's from the States, so they don't know her family. Second of all, she's crazy rich, which is something they respect. But for all that, they can't tell whether they should treat her like they would a duke or duchess.
"Milly, it's true, […] has no natural sense of social values, doesn't in the least understand our differences or know who's who or what's what." (22.214.171.124)
Being from America, Milly has no clue how the British class system works. Maud Lowder actually uses this ignorance to push Merton toward Milly. As far as Maud is concerned, Milly can marry the lowliest commoner, because she doesn't understand class the same way the Brits do, and that's what gives Merton a big chance to cash in on her wealth.