Updating connections weights in neural networks
You actually can increase it by an arbitrary amount. The reason you are increasing it by the sum of all weighted inputs is so that the number you increment by is actually related to the neural network and the input. At least in that case, what you are incrementing by something that is related to what's going on. Otherwise, the behavior may be more random.

There are several functions you could choose to increment by instead. You could also choose to create new neurons (mitosis) where a neuron exceeds an arbitrary threshold. The method you're following is just another method that is being tested in trying to properly represent neural networks.