I remember when I first heard this bit of immature atheistic reductio ad absurdum. I was in high school, and I didn't respond to it because the Nirvana-shirted, long-banged drama stud who said it didn't say it to me. He was laying it on his friend like it was theist's kryptonite.
My answer then, steeped in C.S. Lewis as I was, would have been along the lines of the nonsense of the question as framed. It is a rhetorical and hypothetical "gotcha" with no sincerity behind it, and in any event, it is sort of like asking, "Does the number nine smell red or yellow?"
My answer today is different. My answer today would not be to skewer the nature of the question but to inject its insincerity with the sincerity of God and all the weight of the gospel.
The truth is that God did make a weight so heavy he couldn't lift it. He did so not by building an immovable force -- we did that with our sin -- but by incarnating the frailty of humanity and willingly subjecting himself to the force. As one of us, yet still himself, he created the conundrum of the incarnate God, bearing a cross he both ordained yet could not carry by himself, becoming condemned in death and also victorious. And God was crushed according to the plan he himself projected from the foundation of the world.
So, can God make a rock so heavy even he can't lift it?
Yes. And he did. For three days only. And then he drop kicked it out of the mouth of the tomb.