The key is to think about the actual word "way" and the preposition it implies.
If you talk about a particular way you can go, do you say "it's a way you can go in"? (I know that "a way, in which you can go", would be the grammatically correct phrase, but the former gives the mind a paradigm through which it can gain another path to the meaning).
To my mind, you go through a way.
An example: "Here! Go through this way!"
Yes, yes, people also say, "Here! Go in this way", if they are talking about taking ingress. However, you would still go into a place (which is implicit in the example phrase) through a way:
Example (and most grammatically correct): "Here! Go in through this way!"
So, to my mind, the correct preposition for "way" is "through".
1) That's the way through which the world goes round.
2) That's the way through which I like it.
3) Now we'll consider the two ways through which aircraft can fly.
Now, the first two sound a little weird. But, if you consider that the "ways" in all these contexts are simply a path of events, methods, causes, etc. leading up to/enabling the predication of the result i.e. the world going round/liking it/aircraft flying, this grammar is quite correct.
1) "That's the way through which the world goes round."
Example: "Money makes the world go round"
Extrapolation: The pursuit of money is what motivates society (to move; the
metaphorical world (not Earth) going round).
Paradigm: The pursuit of money (and its pertaining causes) is the causal path to (way
through) which result is the world going round.
2) "That's the way through which I like it"
Example: "I've put that ornament on the mantle, and that's the way I like it"
Extrapolation: "The position of the ornament (as well as the things that led it being there i.e. I having put it there) results in my contentment with where the ornament is"
Paradigm: "Where the ornament has been placed (and the causal path to that) is the causal way through which I have achieved contentment with its location"
3) "Now we'll consider the two ways through which aircraft can fly.
Extrapolation: After having seen, previously, that the "way" through which things are done or exist tends to be an implied matter of a causal 'path to' or 'way through', we can logically surmise that the meaning of this sentence is:
"Now we'll consider the two causal ways through which a path of events can result in the aircraft flying"
A conclusion: We can extrapolate that the word 'way' is often used incorrectly. For example: 'Which way should I go', should be 'In which direction should I go?'. A 'way' is something through which you go. Another example: 'Show me some good ways to bake a cake', should be 'Show me some good methods to bake a cake'. 'Way' often replaces many words, because English is an incredibly, intellectually, lazy language. The same reason is why we have so many phrasal verbs: 'go in' instead of 'enter', 'hang on' instead of 'grasp', 'dig up' instead of 'disinter...', etc
Disclaimer: I have no references for these premises, because it is a theory borne of reason, not evidence. Language is hardly something you can prove through evidence; idioms, for example, are so subjective, and it could be argued that they cannot be based on precedent because anyone at any time could create a new one. Language, especially English, is a constantly evolving form and it perpetually adapts to the thought-structures and meanings which employ it. I would gleefully discuss with anyone who made a cogent, reasoned argument that provides a good basis to dispute what I've written, afore. However, I feel I would be wasting my time to engage with the dogma of an evidence based retort, as the two are incompatible. I hope my perspective can add a colour of light to your own interpretations.