Say, character2 says or does something -- usually stupid in nature -- in which character1 responds with a similar face and a comment of their own. I see this a lot in anime, and I was wondering if it had a name. This happens a lot in Naruto.
Is a visual cue to establish who is the "straight man" in the comedy bit.
Funny man: I Really like ceilings, I guess I am a ceiling fan!
Straight man: ¬_¬
I don't know regarding the facial expressions, but your description of their dialogue seems to be a typical example of boke (character 2) and tsukkomi (character 1) in manzai comedy. This type of humour is typically japanese and can be seen or heard in most variety shows and anime with humoristic tendancies. Anime also tend to have the variation of "boke and boke", where both characters say stupid things.