Several weeks; a period of a few weeks (usually a short term spanning two or more weeks).
申請の結果は数週間かかることが多い。
It often takes several weeks to get the result of the application.
その風邪は数週間続いて治りにくかった。
That cold lasted for several weeks and was hard to recover from.
引っ越しの準備を数週間かけて行った。
I took several weeks to prepare for the move.