Bill Weaver started making scopes about 1930 in Kentucky with two employees.
He moved manufacturing to El Paso Texas in 1933.
The K model in 2.5x and 4x was first introduced after WWII and continued in production until he eventually sold the company in 1968, and died seven years later in 1975.
By the 1960's, the W. R. Weaver Co. had over 600 employees and Weaver scopes accounted for over half all the scopes sold in the U.S.A.
I have never seen a K model with the bare aluminum turret like yours.
All I have seen had a black anodized turret.
So I don't know if that means yours is a very very early one, or if someone polished the anodizing off.
In short, I can't date it any closer then 1950'ish to 1970'ish.
rc