“overlooked” opposite meaning

This is a case where meaning is not separate from its context (it rarely is). A word may have several dictionary definitions but sometimes we can only decide on the correct one by looking at the context. For example, "I saw wood" is ambiguous, whereas "I saw wood with my eyes" or "I saw wood with a sharp tool" both make the meaning of "saw" clear.

There are others examples similar to your question about overlooked. Here are two examples of such antonymic homonyms:

Cleave

= to divide by or as if by a cutting blow : SPLIT “The blow cleaved the victim's skull.”

= to adhere firmly and closely or loyally and unwaveringly

Merriam Webster

Sanction

= to give effective or authoritative approval or consent to

= to impose a sanction or penalty upon

Merriam Webster