Before you even try to read my next post, please study this one carefully. Put the message in your [mental] pocket. To take it out once in a while to play with it. So you will get to understand and know it.
I used http://dictionary.reverso.net/english-definition/ to compare three verbs that are not as much alike as they seem at first glance.
to look underscores were placed by JoAnne Lakefield
The definition of looking is often about guiding either the eyes or view [def. 1, 5 ,11] or the attention [2, 3, 8a, 9] or even conclusion [3, 4, 12] into a certain direction.
But what about result? There are no guarantees: we either hope [6, 7b] or search [7a, 10], without a note about how it ends. Even having recourse to something is inconclusive: it means one is able o make use of something but that doesn't mean he will [8b].
So looking is definitely directive and suggestive, but it is inconclusive.
Watching sounds a lot more careful and aimed at detail, but I sense something stressed or negative too. It's mostly like keeping an eye out for danger, for things to be wary of, to make sure things won't go out of control.
I left out definitions 9, 11, 12, 13 ,14. They are all about seeing a human being. Let's play with it.
Seeing is about experiencing or undergoing. Or about doing a thorough in depth research for a conclusive answer, right. Keep that in mind when you look at these phrases....
Cameras, our mechanical eyes...