Each of the films you describe centers around unusual people who have a supernaturally bizarre trait of some kind. In each case, the characters live on the fringes of society until someone comes along who sees them for their, shall we say, inner beauty, and appreciates them. My favorite example is in Big Fish, where there are a series of characters with odd deformities or proclivities who find solace in each other, and in the one place where it is ok for them to be abnormal- the circus. The same thing basically happens to poor Edward.
There are several things we learn about society from this. First of all, just because someone is different does not make him or her scary. We should get to know people, rather than fear or discriminate against them because they are different. The “freaks” in these films are actually usually gentle and kind despite their initial scariness. In each case, the person who discovers them benefits, and so does the community at large. Let that be a lesson for all of us!