Had a similar problem with my weber. My fuel pump was weak and getting into fourth and fifth gear I was running out of fuel in the bowl. I moved to an electric rotary fuel pump and my problems went away. Make sure that with the weber you have a fuel pressure regulator in line. it really makes a difference in getting it set up and running correctly. hope this helps. there may be other reasons as well. good luck.
I know you think you know what you think I said, but I am not sure you realize that what I said is not what I meant!