I bring this up because I have a tendency to say “thank you” right back, since I was provided service and a meal, but then I feel kind of silly afterward.
I say “thank you” right back also.
I usually say “and thank you as well” or something similar, for the same reason. BUT I don’t feel awkward or silly about it.
Don’t worry you’re cool 
Now, if he is thanking me for a tip or something in particular, I often respond with “you’re welcome”.
Yeah, I’ve noticed lots of people (myself included) respond to “thank you” with another “thank you”. After it happens I think, “What did I/they thank me for?” Enough people do it that it isn’t a big deal.
The weirdest place I’ve encountered it is at work where I’ll ask my supervisor a question and I’ll thank her for her answer, and she will respond with a thank you.
It’s like responding to “thank you” with a “thank you” is some kind of hyper-politeness in society at work. Better to do that than to not respond at all (or have someone else not acknowledge your response). When I tell someone “thank you” for opening a door or something and they don’t respond I wonder if they heard me or not, and don’t want them to think I’m a jerk because they didn’t hear me.
I agree thanking someone for saying thank you is over the top, however much I might want to when someone finally thanks me for holding a door for them, or whatever. “You’re very welcome” or “my pleasure” might do.
But in this case you’ve done something for each other. The waiter’s provided you with good food and good service (hopefully) and you’ve chosen to visit his restaurant, praise the food, and pay for it. I think both saying thank you is entirely appropriate.
A few years back I began with the “You’re Welcome” reply, to airline pilots, restaurant staff as I was leaving, etc… I figure they could use the change of pace, and let them know I was actually listening to them.
I ALWAYS say “Thank You” to the wait staff when we get water, food, rolls, etc… during the meal, or peanuts during the flight. But I see the last one as them thank me for my patronage, supporting their business.
Last time I replied “The pleasure was all mine, thanks”
You’re welcome sounds silly in that situation.
I say, “No, thank YOU!”
What Kalhoun said.
I think that in the interaction of waiter-customer, the waiter is much more deserving of thanks than the customer. I always go out of my way to make badly-paid and overworked service people feel appreciated.
I’d say “thanks”, or if the meal/service was really good, “it was a pleasure”.
Makes perfect sense, they thank you for your custom, you thank them for their good service.
Reminds me of the scene in Lonesome Dove when Newt brings Lori a plate of food then thanks her…stuttering and embarrassed…then thanks Gus for letting him off the hook to get back to the herd.
I even say yes sir, thank you, please to my kids. They do the same with others and have often been complimented on their manners. I figure good manners can’t hurt. 
I’ve fallen into the habit of saying, “You bet!” in such a situation. It breaks up the monotony a bit of always saying a reciprocal “Thank you” or a “You’re welcome.”
I usually smile and say “have a good night.”
“Anytime!”
“No problem!”
“Sure thing!”
I like to mix it up.
I usually just smile and cheerfully say “mmm hmm!” or something to that effect.
I do work at a restaurant (not as a waitress) and I take to-go orders over the phone. After I say “you can pick up your food in X minutes, have a nice night!” the person on the phone inevitably says thank you, and I usually say “thank YOU!”.
But whatever works, any response should be fine!
Simply put, just smile and nod…
Actually, you’ll find that this works not only for acknowledging a restaurant’s gratitude, but also in just about any awkward situation you could imagine.
I say, “Thank YOU.”
He’s thanking me for coming.
I’m thanking him for serving me.
Even trade.
So, you’re the guy I see when I get to town… just grinning and shaking. Folks told me you were a little bit…(hmm, trying to be delicate/sensitive)
different, yeah different’ll work. If you recall I’m the guy with the beard and cowboy hat. I usually just smile back, maybe tip my hat a little to acknowledge you’re at the other end of the bar not saying anything. Kinda like me, enjoying your beer or tequila in peace. 
This response makes me ponder the question…
Whether or not to say thank you after sex? It is obviously and/or supposedly a mutually beneficial arrangement. (w/ possible exception for BJ’s)
This maybe TMI requiring a new thread. :o