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Here is a sentence from her introduction:

I earnestly wish to point out in what true dignity and human happiness consists - I wish to persuade women to endeavour to acquire strength, both of mind and body, and to convince them that the soft phrases, susceptibility of heart, delicacy of sentiment, and refinement of taste, are almost synonymous with epithets of weakness, and that those beings who are only the objects of pity and that kind of love, which has been termed its sister, will soon become objects of contempt.

What are the siblings [sisters] in this long sentence? Here is the part of the sentence which I suppose should give the context. I replace "those beings" with women.

Delicacy of sentiment, and refinement of taste, are almost synonymous with epithets of weakness, and that (women) who are only the objects of pity and that kind of love, which has been termed its sister, will soon become objects of contempt.

My guess is that the pair is "weakness" and "pity." Grammatically, how is "pity" associated with "weakness" in this sentence?

TL;DR: the "siblings" are pity and that kind of love, the latter referring to a love of women that is dependent on them displaying those feminine virtues that mark them as weak.

The best way to tackle a convoluted sentence like this is to break it down into meaningful components. Wollstonecraft starts by saying she wants to point out what true dignity and human happiness consist of, and following the dash, explains this in a different way. Let's look at what's after the dash, and replace the key noun phrases with placeholders to help understand the structure.

I wish to persuade women to endeavour to acquire A, and to convince
them that B [is] almost synonymous with C, and [to convince them] that D will soon become objects of contempt.

Okay, let's look at what A, B, C and D represent:

• A: strength, both of mind and body


• B: the soft phrases, susceptibility of heart, delicacy of sentiment,
  and refinement of taste


• C: epithets of weakness


• D: those beings who are only the objects of pity and that kind of
  love, which has been termed its sister.

So when Wollstonecraft says she wants to convince women that B is almost synonymous with C, she's saying that four qualities that (then) were regarded as 'feminine virtues' (the soft phrases, the susceptibility of heart, the delicacy of sentiment, and the refinement of taste) are defined in terms of weakness.

Well, is that a problem? Isn't the female meant to be the weaker gender? Wollstonecraft doesn't think so: she thinks that such women (represented by "D") will soon become objects of contempt.

The last task, then, is to look at "D" and extract its meaning. The three somewhat abstract components are "those beings" (i.e. women), "that kind of love" (i.e. the love that is dependent on women displaying those feminine virtues that mark them as weak), and "which has been termed its sister" (i.e. which is closely related). Let's put that all together:

D: those women who are only the objects of {pity and its close
relation (love of feminine weakness)}.

So, to answer the main part of the question - what are the "siblings"? - they are pity and that kind of love, where the latter refers to the kind of love that is dependent on women displaying those feminine virtues that mark them as weak.

This is an allusion to what was then, apparently, a fairly well-known aphorism, comparing pity and love. Wollstonecraft puts her own spin on it by limiting the comparison to a certain kind of love. Some other roughly contemporaneous examples (bolding added):

To be the object of pity is a situation very humiliating. For although Pity is said to be sister to love, and a certain degree of tender affection is always mixed with it, there is no doubt at the same time such an inferiority in being pitied as is not consistent with dignity of character.

— "The Hypochondriack" No. XXIX, The London Magazine, February, 1780

The Bard has told us, God of Love!

Thy fav'rite sister is the D_^ove ;

And oft Love's Sister has been styl'd

By Sympathy, sweet Pity's child.

—Samuel Jackson Pratt, "The Dove", Gleanings in England, Vol. II, 1801

Phoe. Did I ever hear the like? Pity is the characteristic of our sex.
Blush. Right, madam, it is the sister of Love.

—Richard Cumberland, "The Natural Son; A comedy, in five acts." Collected in The Modern Theatre; A collection of successful modern plays, Vol. V., 1811

In this context, the sentence wouldn't have been quite so difficult to parse for contemporary readers, who would have been unsurprised to see pity and love termed siblings.

... objects of pity, and (of) that kind of love which has been termed its (pity's) sister...

That is my interpretation.