I don't get it.

It means that the speaker doesnt see any sign of love in the relation they are sharing, rather its only friendship. He also implies that he only wants the person to be his friend and couldn't possibly love her even if she does love him...

The key to understanding the whole thing is "awesome friends." The speaker and the person being told this are already awesome friends. The phrase "I don't see the sights of us" can be shortened to "I don't see us." Shortening the quote further: "I don't see us being being anything more than friends." This can be seen as a good thing. Bad things cannot be described as "awesome." I don't know the context of the quote or the whole story of what you're reading but it seems that the two characters in this scene are really great friends and are sharing a moment that makes one or the other see the importance of having each other in their lives. What book are you reading anyway? It sounds like an interesting book :)

For the one who said it, it means he/ she likes them to be just friends forever. The relationship will not blossom into something romantic. How pathetic.

In my own views, I think it means that he/she doesn't see a bright side or something like that for them when they become more than friends.

Is this some sort of love novel you are reading? If so, it's possible that it's one of those situations where, one partner of the friendship is in love with the other, in which the other only view themselves as friends and no more. This is very common in many love stories, as it is common in real life. Though in real life, people are not as happy go lucky as characters in novels. Because characters in novels are designed to create an impact to the viewer/ reader as intended by the author. If this does occur to you in real life, either cope with it, or fight hard enough to win the other's heart. cheers.