They were not looking at you funny.
The meaning becomes clearer if it is written like this
They were not looking at you in a funny way.
They were not looking at you funnily
In this instance, perhaps Groot didn't like the way someone was looking or staring at them as they were probably not doing anything amusing or entertaining at the time. Although Groot is a tree monster and looks quite adorable in the movie, Groot can be an aggressive and violent character.
The adverb funny is also known as a flat adverb. Some examples of flat adverbs are: fast, slow, quick, soon, and good–although this last one is considered nonstandard by many speakers who prefer to say well, as in “He speaks English well” instead of “He speaks English good.”
What does a flat adverb mean? It means the suffix -ly, typically employed for adverbs, is unnecessary.
A He talks funny
B He talks funnily
Both forms are acceptable and could either mean the speaker talks in an amusing way that makes the listener laugh or the way they talk is a bit strange, weird, or not “normal”. See Lexico's definitions for funny.
If a car engine makes a funny noise, it doesn't make us smile or laugh, we understand that something is peculiar, it's difficult to know what exactly is wrong but perhaps we need to stop off at the nearest garage.