Linking to printed books on archive.org
I occasionally participate in answering academic questions in online forums when I hit a block with getting on with my thesis.


No worries, we all procrastinate (ehm... cough cough).


  I often cite a particular large and well-known academic source in my answers. I have my own copy of this book.


You really don't need to own a copy of a book to cite it: many, if not most, academics borrow the books needed for their work from the libraries. Moreover, its cost is irrelevant to your question.


  I am wondering whether it would be academically unethical of me to link directly to this resource in my answers, given the questionable copyright status of archive.org.


If the archived copy is legal (e.g., the publisher might have released the copyright because they no longer print it), it is certainly ethical to link it. However, I'd avoid referring to the copy if it's legality cannot be reasonably established. In addition, should the copy be removed due to copyright infringement, you would end up with a series of broken links.

It is worth noting that links to books are seldom seen on academic papers, unless a book is exclusively available online. Therefore, the issue is more related to whether or not posting the link online.