"in which weeks" is correct and usable in written English.
It is commonly used to refer to a specific period of time within a longer time frame. Example: "I will be traveling to Europe in July, during which weeks I will be visiting several countries."
Exact(1)
The reason, in a business in which weeks of sea travel is the norm, is time.
Similar(59)
Mothers reported in which week of pregnancy the child was born.
And so began a cycle in which, each week, he courted me and then left me feeling damaged and discarded.
CrunchArcade is a weekly column in which the week's gaming news, reviews, and other games-related tidbits are collected and augmented for your pleasure and convenience.
Otherwise, we'll go on living the farce in which a week with four mass shootings is somehow a good one.
The signals are presented first in a table that displays, for each signaled pathogen, the week in which the increase occurred (by week of sampling), the type of algorithm used, and the epidemiologic week in which the signal was generated.
Every week you think this is the week in which it will happen and every week it's not.
Sometimes weeks went by, though, whole weeks in which he read no pages.
He had barely two weeks in which to do so.
I had two weeks in which to write something.
There are state elections in coming weeks in which the votes of Muslim communities will play a critical role.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com