[snozolli]

It is, in fact, a thing

It isn't. "Grow weary of" is a common phrase. "Grow wary of" are words you can put together, but it's not a common phrase.

I've already posted all the evidence needed, and I grow weary of this misguided argument.

[mkr-hn]

Your lack of familiarity with the phrase and misunderstanding your own source does not actually prove anything.

Here, I'll give you a head start on doing what I suggested.

https://www.google.com/search?q=%22grow+wary%22

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.