English has been steadily losing many of its grammatical "complexities" (or beauty, depending on how much one enjoys grammar).
Thou and thee did not stress respect, to my knowledge. Whoever informed you as such probably felt that way due to associations between those particular pronouns and the King James Bible, which is probably where those pronouns are most associated with today.
Thou was the second-person nominative-cased pronoun. Simply put, it was the second-person form of "he" (subject). Its roots go very far back, but in Old English it was rendered þū.
Thee, on the other hand, was the second-person accusative-cased pronoun (analogous to our third-person "him"). In OE this was þē or þēc. Note that 'þ' is pronounced as a voiceless 'th', like the 'th' in thick.
You also has a similar storied past. It was simply the plural dative-cased second-person pronoun ēow (Old English had different pronouns for singular second person, when you're speaking to one person, versus plural second person, which we render as "you guys"). In modern English we form the dative case of nouns by putting it into a prepositional phrase like 'to you'. This was a single-word form of that.
English has lost many of its grammatical rules regarding case agreement. In concert with that, we've also lost having two sets of second person pronouns. For reasons mysterious, the language evolved this way. According to Google, in the 14th century 'you' began replacing 'ye', 'thee', and 'thou', and by the 17th century 'you' was the primary second-person pronoun for both accusative and nominative cases. Remember we still have the genitive your, which was also from the second-person plural genitive pronoun ēower.