by Mark Kleiman
While "thee" and "thou" (and the corresponding verb forms such as "shalt") sound formal to us because they're associated with the Bible, they were originally the informal or intimate versions of of the second person pronoun, used either with kin and close friends or from superior to inferior.
But we can carry the analysis back one more step. Before "thee" (French "tu," German "du") was informal or intimate, it was singular, while "you" and its equivalents were plural.
At some point, addressing a singular interlocutor in the second person plural became the formal or honorific form. (The connection of plurality with honor is maintained in the royal "we.") Over time, the honorific plural became the normal polite form of address, and the singular was reserved for intimates and inferiors.
That had the unfortunate effect of eliminating the distinction between the singular and plural forms of the second person. In the sentence "I'm coming to see you" it's clear that there's only one of me (else it would be "We're coming...") but unclear whether I'm coming to see you as an individual or a group of which you are one. (The Southern regional "you-all/y'all" filled in this gap neatly, but failed to achieve standard status.)