Technically yes. But the earth rotational speed being 360° per 24h, you get 0.004° per second or 7.27 rad/s. We can then calculate the centrifugal acceleration related to this speed assuming the earth radius is 6371km and neglecting flight altitude. 
$$a_c = \omega^2 r= 0.0337m/s^2$$
So your acceleration is either 0 or 0.0674m/s^2. Compare that to the gravitational acceleration 9.81m/s^2 and you get 0.687% of weight difference either direction compared to your mass staying still at the airport.