Whenever another creature with power 2 or less enters the battlefield under your control, you may pay {1}. If you do, draw a card.
Apply power bonuses from counters the creature enters the battlefield with and continuous effects such as that of Valiant Knight before checking to see if Mentor of the Meek's ability will trigger.
Mentor of the Meek's ability checks the power of the other creature only as it enters the battlefield. If that creature's power is 2 or less, the ability will trigger. Once the ability triggers, raising that creature's power above 2 won't affect that ability. Similarly, reducing the creature's power to 2 or less after it enters the battlefield won't cause the ability to trigger.
While resolving the triggered ability of Mentor of the Meek, you can't pay {1} multiple times to draw more than one card.