The value of rupee is once again seen weakening at the onset of the trading week this morning here, when it went down trading against dollar to Rs81 level. Dollar against rupee at the onset of the trading week in inter-bank market today gaining paisa 40 seen bought at Rs81.05 and selling at Rs81.25. Money market dealers said that the rupee is seen under pressure due to high demand for dollars from the importers. The dealers further said that the value of rupee had surpassed Rs81 last week also during the trading.