You don't want to know my answer.
Ds started the why stage at 35 months (2 years 11 months). He's 6.5 now. And he's still going.
Sample:
We're reading a story about the moon reflecting off of something, and I use the word 'reflection':
Ds: What's a reflection?
Me: Well, it's when light bounces off of something and so you can see it again, kind of like when you look in a mirror.
Ds: Why?
Me: Why what?
The absolute worst was the first year or so -- from age 3 to 4. He would ask why after almost every single thing I said. Even his preschool teachers commented on how often he asked why, and they've seen a lot of kids asking why!
It's died down since then, but he is a pretty incessant question asker. And you're right, sometimes 'why' makes no sense.
Ds: What's that mom?
Me: That's a river, hon.
Ds: Why?

:
Why is that a river????
I find that "why what?" sometimes helps because then it'll make him formulate the real question (why is that called a river? why is there a river there?). He also often uses 'why' when what he really wants to know is 'how', so querying further sometimes brings that out.
Some people have luck with "Why do you think?" but that never worked for my ds. He really did want to know why, it wasn't just a conversational device to get my attention. Mostly, I just answered.
When it got too much, I would declare a break from questions. So, I'm the mom you heard in Target saying "That's it! No more questions until after we're through the checkout line!" People would look at me funny, but they have no idea what it's like to be bombarded by constant questions!