I agree about it not being related to
Lee and
Leigh. Unless it is spelled
Lea and used as a variant (pronounced exactly the same). So
Lea could be a variant of
Lee,
Leigh or of
Leah.
Leah however doesn't have anything to do with
Lee.
I think "weary" is a very likely meaning. In the bible
Leah has "weary" eyes. However people fight whether the "weary" is to be translated as meaning "bad eyesight" or "ugly". We all know that the biblical
Leah wasn't described as an attractive person. Her sister
Rachel was the beautiful one.