Thee would be used to address someone very formally or in a demeaning way if you do know them.
Thee and thou are older than the Elizabethan time, they actually started dying out in the 1600s.
The pronunciation of āthouā was different in different parts of Yorkshire. In [what is now] West and South Yorkshire, it is often spelled āthaā in dialect writing. In the more rural remainder of Yorkshire where I am in the North Riding, it is often spelled as āthooā. In phonetic terms: West and South Yorkshire ưa other parts ưuĖ
āTheeā and āthyā often sounded the same when unstressed as ðɪ. However, they could be distinguished when stressed as ưiĖ and ưaÉŖ (or ưaĖ in some bits of Yorkshire).
Listen here to the North Riding dialect.
Listen - Yorkshire Dialect Society