Commonly, you would say weeks when months wouldn't apply, otherwise it would be misleading if not plain wrong. Usually. (such rules aren't set in stone, allowing humor to exist for instance ("I had a child" "Aw! A boy or a girl?" "Yes"); context matters)
Mathematically true isn't sufficient (and possibly sometimes not even relevant), "weeks ago" bears more meaning in common language than "there exists N such that N > 2 and N weeks passed".
So you were born that many weeks ago, but not really weeks ago.
What matters is how things are understood and it's not usually the interpretation of a formal version of the text (or it is, but a complex one that depends on the mood, the culture and the knowledge of the recipient, their understanding of the author, possibly on other factors as well, that most likely doesn't quite match a naive formal translation)
Mathematically true isn't sufficient (and possibly sometimes not even relevant), "weeks ago" bears more meaning in common language than "there exists N such that N > 2 and N weeks passed".
So you were born that many weeks ago, but not really weeks ago.
What matters is how things are understood and it's not usually the interpretation of a formal version of the text (or it is, but a complex one that depends on the mood, the culture and the knowledge of the recipient, their understanding of the author, possibly on other factors as well, that most likely doesn't quite match a naive formal translation)