Even today, if you have one drop of black ancestry, you're considered black.
Not by everyone. That seems to be your personal standard. When a person is obviously mixed, most Americans say "mixed race." Some "one drop" people look entirely white. Few polite people label them black.
Genetically, the darker DNA seems to "outweigh" the lighter coloring. But not always. Facial features also may indicate ethnic heritage. I come from the school of thought that "content of character" is rthe more important distinction.
Have a look at these mixed-race twins, one parent white, the other black:

Lucy Aylmer, left, and Maria Aylmer are twins, despite their radically different appearance.

Different but the same: a story of black and white twins

Marcia, left, and Millie Briggs are 11-year-old biracial twin sister from Birmingham, England.