Are they all correct?
1)You are looking happy.
2)You look happy.

1)You are looking great.
2)You look great.

I doubt because some textbooks say they all are correct, but some others say that only the second sentences are correct and possible.

Question

Are they all correct?
1)You are looking happy.
2)You look happy.

1)You are looking great.
2)You look great.

I doubt because some textbooks say they all are correct, but some others say that only the second sentences are correct and possible.

Answer

They're all correct, however, the use of the simple form is much more common for these verbs of state.. The use of the continuous forms is optional, and emphasizes that we are referring only to the present moment, and also makes the looking seem almost like an action, rather than a state.