I agree with Jason's comments, that these responses sound (if humorous) are supposed to be interpreted similar to a question where one option is supposed to be chosen from many (usu. with implied mutual exclusivity):
What would you like for dessert, ice cream or cake?
Yes. (Implying that I don't want one option, but rather all options)
By answering with purposefully incorrect English, the speaker is trying to give a humorous response.
It seems like an extension of that, for example in the first one:
Engineer: "How large should the rims be on the new model?"
I take it to mean "Yes, they should be very large, so large that they are almost indescribably/ridiculous for the context". This does not have the implication that the speaker is "high/stupid/not able to speak the language well" in this case, but rather that the speaker is trying to describe an "indescribable" aspect. So instead of giving a proper answer, they give a "joke" answer.
This kind of joke would be strange in this case, since the rims of a car can only be so big. It might apply better to someone designing a Monster Truck, and asking how big they should make the wheels. For example if the engineer is used to designing regular cars that are much smaller, then the person saying this would be implying "way, way bigger than you expect". It is still not the best use of the joke however.
In the second one:
Buddy: "How much weed are you taking with you?"
Snoop Dogg: "Yes"
I would say that this is supposed to imply that the speaker is "high" (mostly because being Snoop Dogg already has that implication). But there is also the implication, since the Buddy asks "how large of an amount", that the answer has an implied "So much weed that it's ridiculous".
In general, I would say that it sounds pretty characteristic of young people "Internet Speak", of people trying to apply a format of a joke they see often in other circumstances. In cases where a "degree" question is asked instead of between a few options, the implication is usually too such a high degree that it is indescribable/funny/ridiculous.
However, most of the humor comes from being it being a reference to the original joke format, rather than being funny by itself. It sounds like what my 10 year-old cousin might use when talking with his friends about Minecraft/Fortnite/whatever else they come up with.