Checkers playing Neural Network evolved with Genetic Algorithm becomes too sensitive to input data changes
Full disclosure, I'm not at all an expert on genetic algorithms, so take this with a grain of salt.

First of all, I'm not sure the $r$ parameter in $w'=w*m'*r$ makes sense. You say it's a random standard Gaussian number, which means it could totally change the sign of $w'$. That seems bad. Am I understanding that correctly?

That aside, answering your actual question of controlling weights that get out of control: I would re-normalize the weights after each iteration, e.g. by dividing by its norm: $w'' = w' / ||w'||$. This will allow the weights to shift around, but will keep them from exploding.