There is evidence of usage for several variations:
The Quality Standard Subcometee recommends treatment... within 4 weeks... of symptom onset.
from: Textbook of Peripheral Neuropathy
(I cut out the medical details which were unimportant for this question.)
Within several weeks of the opening of school we heard replies from all...
from: The School within Us: The Creation of an Innovative Public School
By James Nehring
Conjunctivitis is common, and corneal opacities can occur but usually resolve within 6 weeks after cessation of therapy.
from: Textbook of Therapeutics: Drug and Disease Management
edited by Richard A. Helms, David J. Quan
The person notified can file an objection to the Minister of Finance, within six weeks from the date of the decision taken by the Minister.
from: Global Forum on Transparency and Exchange of Information for Tax Purposes... by OECD
It is perhaps worthwhile noting that most vertebral fractures heal within 6-12 weeks from injury.
from: Spinal Trauma - An Imaging Approach By Victor N. Cassar-Pullicino, Herwig Imhof