What is the difference between "You are looking well" and "You look well"?

Solution 1:

Both of those are acceptable English. In essence they are the same, meaning that you are looking healthy. The first is continuous present, which implies an ongoing state, the second is present, which only describes how you look right now. In almost all cases the two can be used interchangeably. An example of when it might be wrong to use the first is when the state is changing - for example you see someone in a poor light and remark "You look ill". Then they turn on a brighter light and you say "You look well now".

The contraction in the first makes it less formal, but "You are looking well" would restore the formality.

(As an aside, beware of "you are looking good" which does not mean the same as "you are looking well")