"How much weight does a recommendation from a well known author help a beginning writer in the query process?"
The answer: (relevant to the slush submission process, too)
About as much weight as anything else that might make the editor sit up and take notice of you, which is some. But then, it could backfire on you. I'll explain later.
But let me elaborate.
First, using gimmicks to make the editor notice your submission is always a bad idea. Things like submitting on colored paper, or submitting in strange font formats. For the most part, editors just want the regular old stories submitted the regular old way--on white paper, Times New Roman or Courier New font, double spaced, 1" margins, blah, blah, blah.
Second, what you DO want to include to make the editor sit up and take notice is what you'll include in the content of your cover (or query) letter.
I want to be informed. I want to know who you are. Quite a lot of authors don't put their full name on their submission letter. Do it. It introduces you to me. It makes you real. It makes you an author, just like me, who's trying to make a name for herself, so don't be hesitant to make your name known. It's that simple. You don't need to give me a biography at this point. Just your name is good for now. If I want to pursue the relationship (ie. I request your story via your query, or decide to publish your story) then I might want to know a little more about you. And in the case of a request via query, I'll tell you what more I want to know. But for the preliminary process, I just want a name. I don't care where you put the name. At the beginning as an header or at the end as a signature or both. It doesn't make much difference.
I want to know that you respect me and the work I do. Begin your letter respectfully. A simple, etiquette-pure 'Dear Editor,' is a beautiful beginning to a query/cover letter. Follow that up with a line that explains what you are writing to me about. My personal cover letter begins this way: Dear Editor, I respecfully submit my story, "Name of Story," for your consideration. That's all. That simple. Most editors, myself included, don't give cover letter much more than a cursory glance/quick read. I scan over cover letters to see if the story title is there, if the writer's name is there, if there are some important details that might put that letter above some of the others, or that I might want to give special attention to. Which leads me to...
I want to know what you've done. Quickly summarize your most recent and/or impressive publications (for example, a publication in Analog is going to draw considerably more attention than a publication in a non-paying ezine, but considerably less attention if that Analog publication occured in 1972), any writing workshops you've attended, pertinent college background--like if you have a degree in English or Creative Writing. If you're a sci-fi writer a degree in Ethnobotany is interesting and fairly pertinent. It shows me you know your science (or should). But telling me you have a degree in Accounting and your story is a historical romance set in Ancient Babylon, the Accounting degree carries no weight whatsoever.
If you have no such experience (publication, workshops, college) just omit it. A simple respectfully submitted letter is better than saying you have no experience. Best for the editor to wonder at it.
It would be at this point, for my questioner, that you would insert the recommendation from the author.
But is that recommendation a gimmick? Or is it a legitimate point of reference and qualification?
I don't know. I've never come across this question or the answer to it in my years of writing and editing.
I think it could be taken either way. But let me share with you my thoughts:
1. How do I, as the editor, know that this recommendation is a legitimate one? If you can get a signed letter from the well-known author to include with your query/cover, that's one thing. As an editor, I'd want to also have the well-known author's contact information so I can check up on it. You see, I can fairly easily check up on your publication and workshop credits. If I'm really ambitious I can check up on your college degree credits without too much trouble. But it's not as easy to check up on your say-so that Well-Known Author likes your writing or your story.
2. I'd let such a recommendation carry more weight if it were applicable to the individual story, rather than you or your writing in general. As an editor, I look at stories more than authors or their qualification. Your story is what sells you. At least to me. And I think that's true of most editors in the magazine industry. It might be a whole 'nother ball of wax for the book industry.
3. Make sure you're submitting appropriately, or your recommendation will get you less than nowhere. For example, your story can be recommended from here to eternity, but if you submit a novelette to a flash fiction market it's not going to look good for you OR the author who recommended you. So use that recommendation with care. Make it count. Protect it and preserve its value by using it wisely.
4. Use it humbly. Be very careful you don't make the editor feel as if you're demanding publication because of your hoity-toity recommendation from Well-Known Author. Remember, magazines reject stories from professional authors all the time. I say again, it's not you, it's your story that sells you.
5. Weigh carefully the value TO YOU of that recommendation. Why? Because some editors may see it as presumptuous. You never can tell. Editors are editors. They're as individual as snowflakes under a microscope. They have prejudices, preferences, and burrs under their saddles, just like everyone else. If the editor who sees your query happens to LOVE the author who wrote your recommendation, then you can't lose. But what if the editor happens NOT to like the author? Not so great. So, do you want the recommendation to sell your story? Or do you want your story to sell your story? The recommendation MAY very well help. That's good. But ultimately it will always be the story that seals the deal.
I hope that answers your question, or at least gives you some food for thought. I'm going to put the word out on my writer/editor network and see what other's have to say. I'll include those comments--if any--in the comments for this post. If you need clarification feel free to ask for it.