weights in a simple neural network
It's just that the logistic function reaches its saturated regime around +-4.6, as in the image. So, any absolute values of x much lower than this will give you results around 0.5. Increasing the absolute value of the weights (all of them) you'll get nearer the saturated region, resulting in outputs closer to 0 and 1. Nevertheless, if you use the step function at the output layer instead of the logistic, you'll get the correct values exactly for both sets of weights: 0 0 0 1.