Question: It is a frequent idiom for a group of characters to interact while eating Chinese food. Generally of the carry out variety, with chop sticks being plunged into the deep fold-up boxes. It seems to me that this is intended to bring a particular thematic element, but I can't quite put my finger on it. I see it way too often for it not to have a specific significance.

Answer: 
I think sometimes people look for symbolism a little too much in cinema. In this case, I contend that there is **no** symbolism in Chinese food. It just happens to be an easily recognizable take-out food that can be recognized without branding. Also, hamburgers or pizza have been used but there are a lot of challenges with that. You have to control the environment, and when someone takes a bite you can't just replace it. But if you throw some rice or noodles in a box and someone takes a bite, you can refill it.
I think that movies and TV shows use those Chinese takeout boxes just because it’s easy for production. They could be empty boxes and they wouldn't actually have to prepare any food for the scene or multiple scenes at that.