If you ban weaving, then we are going to end up with freeze frame video stills being posted in internet forums all over the world with fans trying to prove that a driver was or was not weaving, and F1 would probably have to setup a weaving committee to define what constitutes an unacceptable weave.
I assume speeding up or slowing down would similarly be banned.
You could take the whole thing out of the drivers hands - set them at pit limiter speeds until a green flag waves, and then go go go, overtake if you can.