In 99% of cases,
look at means something roughly like
try to see, make an effort to see, direct your powers of sight toward, attend visually.
In comparison,
see is relatively lacking in effort. (There is no form
see at.)
When you
look at something, you actively do something. You pay attention with your eyes.
When you
see something, you simply react to it. Its presence is simply noted. You notice it with your eyes.
Because
look at is a more active process, we can
look at things closely, just as we can examine things closely. But it doesn't make sense to say that we
see things closely.
look at is more like
examine;
see is more like
notice.
-- Do you
see the book on the table?
-- Yes, I
see it. (I am able to see. I am not blind. I see that the book is there on the table.)
--
Look at the book. (Direct your attention toward the book.)
-- I
am looking at the book. What's so special about it?
-- No. You
are not looking at it closely enough.
Look at the cover. Don't you
see that it is damaged?
-- Oh, yes. Now that I
look at it more closely, I
see that the cover of the book is damaged.
CJ