You said it's not a thing. It is, in fact, a thing. I've heard it and said it often enough to be sure it's not so uncommon that it's reasonable to say it's not a thing.
You also need to keep in mind what Google Ngram is.
>> "When you enter phrases into the Google Books Ngram Viewer, it displays a graph showing how those phrases have occurred in a corpus of books (e.g., "British English", "English Fiction", "French") over the selected years."
It's a collection of books. Books remain relevant, but it tells you nothing of usage outside that. You only have to run a search on Google to see that it's used in a wide range of unrelated contexts. It's not some obscure anachronism or regionalism.
Much like how irregardless is now considered a thing. One of these days "mute point" will be a thing too :). I better not look that up, maybe it already is. I often wonder what people think they're saying when they misuse phrases like that.
Grow weary (tired of) and grow wary (suspicious of/concerned about) are different things though. Irregardless is a modification of the already useful regardless. I'm not sure how they're comparable.
That sure looks like a phrase used across a wide range of contexts and unconnected fields, too wide to support any notion that it's obscure. There's even a non-English news outlet using it in its English coverage.
Even if that's the case, it's very easy to hear "grow weary" and conflate it with the similar word "wary", coming up with "grow wary" as a malapropism.
https://books.google.com/ngrams/graph?content=grow+wary&year...