Yes, you can just say "This is really weird" or you could say "this is getting really weird" but we wouldn't usually say "This is really being weird." It's not technically incorrect, but no one will say that under most circumstances (unless you're talking about a machine that keeps malfunctioning or something).
Likewise, we wouldn't generally say "I am being interesting in American movies" because 1) you need a past participle if you're using interesting sort of like an adjective (interested) and 2) the continuous sense is sometimes implied for this type of sentence with a simple being verb and adjective.
For example, you could just say "I am interested in American movies." Other examples are:
"He is thrilled to receive his acceptance letter", or "She is happy to help you." Even though these actions are going on over a period of time, maybe even still going on when the speaker is describing them, the progressive sense is implied.