For instance in text books -more precisely audiobooks- like Uncle Tom's Cabin, and some others that I can't recall now, I've heard the word "thee" when the speaker meant to say "you".
I wonder if this is a more respectful way of saying "you", something like "usted" in Spanish vs "tú"?
No.
Firstly, "thou"/"thee" is not modern English outside of dialectal usages (which I believe is its context in Uncle Tom's Cabin).
Secondly, you're right about the parallels to the two pronouns in Spanish, but "you" is the polite, formal option. Actually, Spanish is a bit more complicated, because it has (I understand) familiar and formal versions for both singular and plural. English is more similar to French; in both languages, the singular ("thou", "tu") is also the familiar, and you would use the plural ("you", "vous") to an individual if you wanted to be formal.
(Related reading: "T-V distinction".)
Thirdly, having said "no", let me now change it to "no, except when it is". Thanks to "thou" falling out of usage, most people are only familiar with it in old works, especially the King James Bible and Shakespeare's plays (both Early Modern English, from around 1600). The former, in particular, has caused "thou"/"thee" to be associated with formal situations, because God is addressed as "thee" (because it's singular, not because it's familiar).
However, that only applies to people affecting old-fashioned usage. They are quite likely to use "thou"/"thee" as a formal pronoun. People who use them because it's part of their dialect will, I'm sure, be using them with their original (singular and familiar) meaning.
Thee and thou were once forms of address which were non-formal and intimate, hence the usage in the Bible and in wedding vows, so they would not originally have been used to denote respect to, say, strangers. However, they came to be used in literary works to indicate that the speaker is ill-educated and doesn't know when to use the correct form for the social situation; they are "overly-familiar", often due to being good-natured. This latter is probably the intent for at least some of the uses in Uncle Tom's Cabin.
The words can also be used in an insulting way, to suggest that the object is not worth a formal address.
As the words fell out of usage they became associated with old-fashioned speech and, as often happens, old-fashioned speech was itself associated with stiffness and formality. So a modern native English speaker will often have exactly the opposite understanding to the correct one - that "thee" and "thou" are especially formal instead of being friendly or relaxed pronouns for use in private situations with friends, children, and lovers.
A final complication is that regional (that is, English spoken in different parts of the UK) English contains these words even today but in my experience they are mostly used in the belittling/insulting manner but with an undertone of jokiness or teasing.
