Well, לֵב and its collateral form לְבָב have the plurals לִבּוֹת and לְבָבוֹת. Modern usage prefers as the prose standard forms לֵב and לְבָבוֹת and uses לִבּוֹת as the contruct form (לִבּוֹת־נָשִׁים hearts of women). It behaves now like nouns as צֵל "shadow" (pl. צְלָלִים) or צַד "flank" (pl צְדָדִים). The underlying doubled second radical (ל-ב-ב) manifests itself: 1) All three are there (לְבָבוֹת), 2) The consonant is doubled with a dagesh (לִבּוֹ my heart lib-bo) or 3) there is compensative lengthening of the vowel (libb -> lev).
Not quite. The word ליבות is not the plural of לב. Only לבבות is the plural of לב, and that is because the 3-letter root of לב is ל-ב-ב.
The word ליבות is feminine and it is the plural of ליבה, which is derived from the same root, but means core as in:
מעבד מרובה-ליבות -- multi-core processor
Well, this is what I said, that Modern Hebrew does not use as standard plural for "hearts" לִבּוֹת as in the Bible (שאול ואבדון נגד יהוה אף כי לבות בני אדם "Sheol and Abaddon lie open before the LORD; how much more the hearts of the children of man!") and uses לְבָבוֹת now. This gave wider room for the word לִבָּה meaning core from the same root. I suppose לִבּוֹת had already there a poetic ring.
Thank you for the excellent reply. You were polite enough not to point out that I had misspoken in my question. This was of course about the doubling of vet, not vav. I had posted the question in Aug, 2018, but I didn't see your answer till just now when I am repeating many lessons. I guess what I'm still wondering is, on these examples you've given, are they really 2-letter roots as opposed to the usual 3-letter shoresh? So they double the second one just to sync with other words? Where does this come from?
Well, it appears that the basic stock of Semitic vocabulary had many root morphemes of a single morpheme like אָב father or חוּד seize!, and that later, when the language developed many patterns to form nouns and verbs, which required slots for three consonants (like XaXaX for 3. perfect qual, XiXel for pi'el), there was a strong pressure on the then two consonantal roots to adopt a third consonant, be it by doubling the second, add a weak consonant at the beginnnig, the middle or the end, or even by adding a modifier to a base meaning, like probably you have with -פר divide, becoming פרד separate, פרם to tear open, פרס split, פרץ break, פרק tear away, פרר break, violate, פרש keep off, ... So it was both a means for variation and more regularity, but this happened mostly in historic times, before we have records of ancient Hebrew.
Consider the Shema Yisrael שמע ישראל: You shall love the Lord your G-d "b'chól levav'chá, u'v'chól nafshechá u'v'chól me'odécha...." וְאָ֣הַבְתָּ֔ אֵ֖ת יְהוָ֣ה אֱלֹהֶ֑יךָ בְּכָל־לְבָבְךָ֥ וּבְכָל־נַפְשְׁךָ֖ וּבְכָל־מְאֹדֶֽך... I guess it comes from the Bible, all right. Deuteronomy (Devarim) 6:5.