I understand the feeling! I mean, on one hand, I know that it's developmentally appropriate, and it's a GREAT learning tool for a 3yo to ask "why" about everything.
But on the other hand, it drives me CRAZY to hear the word "why" in response to just about everything I say! lol.
I try to answer most of them, even if they are 'repeats' or I think that ds should know. I've noticed that he likes to hear things explained a few times, in different ways- I'm sure that helps him actually learn the answers.
But I think sometimes he says why just to hear himself talk. hehehe. In those cases, sometimes I'll do the "what do you think" or I'll just give him a blank stare, like "are you seriously asking me that?"
I'll say something like "Be careful with your juice. It could spill and make a big mess" and he'll say "why." Um...why what? lol.
Sometimes I ask him if it's something he really wants to know the answer to, and if he says yes I do my best to answer it. That actually has given me a lot of insight- there have been a few things that I've thought were just saying why to say why, but he's honestly had a question about the situation.
Sometimes I answer "it just is the way it is" for something that I really don't have an answer as to 'why" I just know that it IS.
Oh yeah, the pp reminded me that sometimes I sing the Wizard of Oz song: Because because because because because, because of the wonderful things he does. We're off to see the wizard, the wonderful wizard of Oz. etc etc.