I regularly refer people to A.W. Pink’s observations on the New Testament use of κόσμος in Appendix III of his book, The Sovereignty of God. The motivation for his study is as follows.
Many people suppose they already know the simple meaning of John 3:16, and therefore they conclude that no diligent study is required of them to discover the precise teaching of this verse. [But] the word “kosmos,” and its English equivalent “world,” is not used with a uniform significance in the New Testament. Very far from it. It is used in quite a number of different ways. (253)
Below is Pink’s list of uses with a “tentative definition” and the verses he references (updated by myself to the ESV).
1. “Kosmos” is used of the Universe as a whole.
The God who made the world and everything in it, being Lord of heaven and earth, does not live in temples made by man. (Acts 17:24)
2. “Kosmos” is used of the earth.
Now before the Feast of the Passover, when Jesus knew that his hour had come to depart out of this world to the Father, having loved his own who were in the world, he loved them to the end. (John 13:1)
“‘Depart out of this world” signifies, leave this earth’ (254).
even as he chose us in him before the foundation of the world, that we should be holy and blameless before him. (Ephesians 1:4)
“This expression signifies, before the earth was founded–compare Job 38:4” (254).
3. “Kosmos” is used of the world system.
Now is the judgment of this world; now will the ruler of this world be cast out. (John 12:31) Compare Matthew 4:8 and 1 John 5:19.
4. “Kosmos” is used of the whole human race.
Now we know that whatever the law says it speaks to those who are under the law, so that every mouth may be stopped, and the whole world may be held accountable to God. (Romans 3:19)
5. “Kosmos” is used of humanity minus believers.
If the world hates you, know that it has hated me before it hated you. (John 15:18)
It’s unlikely that the inanimate parts of the world “hate” Christ, so “world” must be limited to the world of humans. And “Believers do not ‘hate’ Christ, so that ‘the world’ here must signify the world of un-believers in contrast from believers who love Christ” (254).
By no means! For then how could God judge the world? (Romans 3:6)
“Here is another passage where ‘the world’ cannot mean ‘you, me, and everybody,’ for believers will not be ‘judged’ by God, see John 5:24. So that here too, it must be the world of un-believers which is in view” (254).
6. “Kosmos” is used of Gentiles in contrast from Jews.
Now if their (Israel’s) trespass means riches for the world, and if their failure means riches for the Gentiles, how much more will their full inclusion mean! (Romans 11:12)
“Now how the first clause in italics is defined by the latter clause place in italics. Here, again, ‘the world’ cannot signify all humanity for it excludes Israel!” (254)
7. “Kosmos” is used of believers only.
“John 1:29; 3:16, 17; 6:33; 12:47; 1 Corinthians 4:9; 2 Corinthians 5:19. We leave our readers to turn to these passages, asking them to note, exactly what is said and predicated of ‘the world’ in each place” (254).
Pink summarizes: “Thus it will be seen that “kosmos” has at least seven clearly defined different meanings in the New Testament” (255). Regardless of one’s conclusions about “kosmos” in John 3:16 (though Pink makes his conclusion clear), the referent shouldn’t be assumed.