The phrase "for another three weeks" is correct and commonly used in written English.
Example: "I won't be fully recovered for another three weeks, so I'll have to miss the concert next weekend."
His body remained alive for another three weeks.
First cuts will not come for another three weeks.
To stay funded: The U.S. government, for another three weeks.
Rodgers was headed for another three weeks of irrelevance, of remaining an observer and cheerleader.
Bill Clinton is not giving away his daughter Chelsea's hand in marriage for another three weeks.
He was, after all, not expected to make his debut for another three weeks.
"He needs to remain inactive but for core exercises for another three weeks," General Manager Sandy Alderson said.
"I let it stay up for another three weeks, and it was in perfect shape," she said.
After an initial four-week run the play was scheduled to reopen on Wednesday for another three weeks.
Arsenal are set to be without Mikael Silvestre for another three weeks because of a thigh problem.
As airspace is opening up, expecting us to stay here for another three weeks at our own expense is ridiculous.
