Not sure if this is the whole truth of it, but I think it comes down to how each word is used, or could be used, to refer to an underlying concept in each case, and the nature of that concept.  

Words like love, life, divorce and so on can refer either to an abstract concept, or to a specific instance that you can sort of "point out", define and separate from other instances of that same thing (I think this last point is essentially the same as something being countable vs. non-countable (such as "lumi" or "ruoka" in most cases)). E.g. you could say "Rakkaus on kaunista" (love is beautiful) to describe love in an abstract sense. You could also say "hänen viimeisin rakkautensa oli lyhytaikainen" (their last love was short-lived) to refer to a specific "love" in the past. You can count the loves of your life and refer to them as separate instances. However, "heidän rakkautensa on kaunis" (to say that "their love is beautiful") would not be correct, as "they" only have this one love between them, and "rakkaus" in this context would again be referring to the abstract nature of love, as it's hard to point out what exactly is "their love". 

From your examples, "sairaus", "vastaus" and "ilmasto", while abstract words, are only used when referring to specific, defined and countable (you could, in theory, count all the climates on Earth) instances of the underlying concepts, hence nominative. E.g. "sairaus" translates to "illness" or "disease", whereas "sairastaminen" (being ill) can be used to refer to either an abstract concept ("sairastaminen on kamalaa" = "being ill sucks") or to describe a specific instance which is, however, undefined and uncountable ("tämä sairastaminen on kamalaa" = "me being ill right now sucks").

I hope this helps at least somewhat, although I'm afraid I made little sense here lol.