You can read this:

Atanu Shome

https://plato.stanford.edu/entries/word-meaning/

There is some research comparing the brain's of psychopaths and non-psychopaths when shown words of affection and cold words such a brick.look up Prof Robert Hare.

Use "Semantic differential" (Charles Osgood)

You can read this:

Atanu Shome

https://plato.stanford.edu/entries/word-meaning/

I am not sure that you can prove that one word is better than another, but you can set criteria to judge against.

For example, in the context in which you use it, "chill" is slang and "enjoy" is not. "Observe" is more elevated vocabulary than "see." Elevated vocabulary that is not slang could be among your criteria for evaluating language.

But which vocabulary is best depends on the situation. In some situations, "chill" may be arguably better, or more appropriate, than "enjoy."

In addition to previous responses-

The OBJECTIVE with communication is to be UNDERSTOOD. For example, conversing with exhibit A (related to career field) with exhibit B (unrelated career field) speaker would incorporate a universal vocabulary in order to reach an understanding exhibit B can identify with (my concept).

This method is called "CODESWITCH."

In RATIOLANGUISTICS HOW LANGUAGE SHAPES OUR IDEAS ABOUT RACE by Samy H. Alim, researchers identify dialect variations of an isogloss (land boarders).

What about LINGUISTIC CAPITAL from Bourdieu? Still it is very hard to operationalize it... as already mentioned: value of the phrase is always contexualized (regarding style or even language, the speaker in general etc.).

This is a good question. This matter is important when the writer or translator needs to use collocations. I suggest you do some reading on the field of semantics.

This is an interesting question. Without going too technical, and as a starting point for discussion/reflection, I would simply argue that some words are less specific, more general than others, so that they can be used in many different contexts without the need to be very precise. However, if a well-educated speaker, or writer, and in a formal context, may wish to be more precise and to use the best possible word to describe the situation, action, event, quality, etc.

This can also be applied to the use/misuse of modifiers: you can certainly say "I'm very tired" in informal contexts, and everyone will certainly understand, but if you say or write "I'm exhausted", you'll show a better grasp of the English lexicon and being able to use one word that actually express the meanings of two or more words (very/really/extremely) that are somehow empty, because they can be used to amplify basically any word: sad/very sad; angry/very angry, etc.

In the case of verbs such as "see" vs. "observe" that you mention, the situation in similar: you can use "see" in many contexts and meaning different things, but if you want to be more precise, or technical, or stylistically more refined or varied, you may wish to use verbs that have a more precise meaning, such as "observe", or, within higher register, "scrutinise".

The point is to pick the "right" word in context; it's a matter of context and not absolute truth. Hope this helps.