That's very sweet of you in the US sound like
That's very sweef you?
of is only speak
f and link with
I believe what you are hearing is just an example of "connected speech". When anyone speaks in their native language they do not stop after each word, but one word naturally runs into the next. To a British English speaker like myself, many American pronunciations of the letter 'T' sound more like a 'D'. As it is easier for a 'D' sound to merge with the 'F' sound in "of", you are probably noticing this more with American accents that with British.
If you replace the "f" with a "v," then yes, kind of. By "kind of," I mean that it's definitely possible, but it's probably not common, so you should not think of it as the normal US English pronunciation.
I assume that you mean "sweev you" (since "of" ends in a /v/ sound). It wouldn't be weird if an American English speaker didn't pronounce the final consonant in "sweet" and said something that sounds like "swEE-uv-you," with three syllables. (In the International Phonetic Alphabet (IPA), this would be spelled [swi-ʌv-ju].) And then the first two syllables could be somewhat blurred together so that it sounds almost like one syllable, "sweev" (IPA: [swiv]).
More commonly, though, it'll sound like "swEE-duv-you". In American English, /t/ often turns into what's called an alveolar flap, something that sounds an awful lot like /d/ (IPA: [swi-ɾʌv-ju]).